1. CJM Online first
 Fahrner, Anne; Hausen, Jürgen

On intrinsic quadrics
An intrinsic quadric is a normal projective
variety with a Cox ring defined by a single
quadratic relation.
We provide explicit descriptions of these
varieties in the smooth case for
small Picard numbers.
As applications we figure out
in this setting the Fano examples
and (affirmatively) test Fujita's
freeness conjecture.
Keywords:Fano variety, Cox ring, Mori dream space, intrinsic quadric Categories:14C20, 14J10, 14J45 

2. CJM Online first
 Achar, Pramod N.; Riche, Simon; Vay, Cristian

Mixed perverse sheaves on flag varieties for Coxeter groups
In this paper we construct an abelian category of "mixed perverse
sheaves" attached to any realization of a Coxeter group, in
terms of the associated EliasWilliamson diagrammatic category.
This construction extends previous work of the first two authors,
where we worked with parity complexes instead of diagrams, and
we extend most of the properties known in this case to the general
setting. As an application we prove that the split Grothendieck
group of the EliasWilliamson diagrammatic category is isomorphic
to the corresponding Hecke algebra, for any choice of realization.
Keywords:perverse sheaf, flag variety, Coxeter group Categories:14F05, 20C08, 20F55 

3. CJM Online first
 Iacono, Donatella; Manetti, Marco

On deformations of pairs (manifold, coherent sheaf)
We analyse infinitesimal deformations of pairs $(X,\mathcal F)$ with
$\mathcal F$ a coherent sheaf on a smooth projective variety $X$
over an algebraically closed field of characteristic $0$. We
describe a differential graded Lie algebra controlling the deformation
problem, and we prove an analog of a MukaiArtamkin Theorem about
the trace map.
Keywords:deformation of manifold and coherent sheaf, differential graded Lie algebra Categories:14D15, 13D10, 17B70, 18G50 

4. CJM Online first
 Bosser, Vincent; Gaudron, Éric

Logarithmes des points rationnels des variÃ©tÃ©s abÃ©liennes
Nous dÃ©montrons une gÃ©nÃ©ralisation
du thÃ©orÃ¨me des pÃ©riodes de Masser et WÃ¼stholz
oÃ¹ la pÃ©riode est remplacÃ©e par un logarithme non
nul $u$ d'un point rationnel $p$ d'une variÃ©tÃ© abÃ©lienne
dÃ©finie sur un corps de nombres. Nous en dÃ©duisons des
minorations explicites de la norme de $u$ et de la hauteur de
NÃ©ronTate de $p$ qui dÃ©pendent des invariants classiques
du problÃ¨me dont la dimension et la hauteur de Faltings de
la variÃ©tÃ© abÃ©lienne. Les dÃ©monstrations reposent
sur une construction de transcendance du type Gel'fondBaker
de la thÃ©orie des formes linÃ©aires de logarithmes dans
laquelle se greffent des formules explicites provenant de la
thÃ©orie des pentes d'Arakelov.
Keywords:periods theorem, abelian variety, logarithm, Gel'fondBaker method, slope theory, NÃ©ronTate height, interpolation lemma Categories:11J86, 11J95, 11G10, 11G50, 14G40 

5. CJM Online first
 Camere, Chiara; Garbagnati, Alice; Mongardi, Giovanni

CalabiYau quotients of hyperkÃ¤hler fourfolds
The aim of this paper is to construct CalabiYau 4folds as
crepant resolutions of the quotients of a hyperkÃ¤hler 4fold
$X$ by a non symplectic involution $\alpha$. We first compute
the Hodge numbers of a CalabiYau constructed in this way in
a general setting and then we apply the results to several specific
examples of non symplectic involutions, producing CalabiYau
4folds with different Hodge diamonds. Then we restrict ourselves
to the case where $X$ is the Hilbert scheme of two points on
a K3 surface $S$ and the involution $\alpha$ is induced by a
non symplectic involution on the K3 surface. In this case we
compare the CalabiYau 4fold $Y_S$, which is the crepant resolution
of $X/\alpha$, with the CalabiYau 4fold $Z_S$, constructed
from $S$ through the BorceaVoisin construction. We give several
explicit geometrical examples of both these CalabiYau 4folds
describing maps related to interesting linear systems as well
as a rational $2:1$ map from $Z_S$ to $Y_S$.
Keywords:irreducible holomorphic symplectic manifold, HyperkÃ¤hler manifold, CalabiYau 4fold, BorceaVoisin construction, automorphism, quotient map, non symplectic involution Categories:14J32, 14J35, 14J50, 14C05 

6. CJM Online first
 Shimada, Ichiro

On an Enriques surface associated with a quartic Hessian surface
Let $Y$ be a complex Enriques surface
whose universal cover $X$ is birational to a general quartic
Hessian surface.
Using the result on the automorphism group of $X$
due to Dolgachev and Keum,
we obtain
a finite presentation of the automorphism group of $Y$.
The list of elliptic fibrations on $Y$
and the list of combinations of rational double points that can
appear on a surface birational to $Y$
are presented.
As an application,
a set of generators of
the automorphism group of the generic Enriques surface is calculated
explicitly.
Keywords:Enriques surface, K3 surface, automorphism, lattice Categories:14J28, 14Q10 

7. CJM Online first
 Scaduto, Christopher W.; Stoffregen, Matthew

The mod two cohomology of the moduli space of rank two stable bundles on a surface and skew Schur polynomials
We compute cup product pairings in the integral cohomology ring of the moduli space of rank two stable bundles with odd determinant over a Riemann surface using methods of Zagier. The resulting formula is related to a generating function for certain skew Schur polynomials. As an application, we compute the nilpotency degree of a distinguished degree two generator in the mod two cohomology ring. We then give descriptions of the mod two cohomology rings in low genus, and describe the subrings invariant under the mapping class group action.
Keywords:stable bundle, mod two cohomology, skew schur polynomial Categories:14D20, 57R58 

8. CJM Online first
 Hartl, Urs; Singh, Rajneesh Kumar

Local Shtukas and Divisible Local Anderson Modules
We develop the analog of crystalline DieudonnÃ© theory for $p$divisible
groups in the arithmetic of function fields. In our theory $p$divisible
groups are replaced by divisible local Anderson modules, and
DieudonnÃ© modules are replaced by local shtukas. We show that
the categories of divisible local Anderson modules and of effective
local shtukas are antiequivalent over arbitrary base schemes.
We also clarify their relation with formal Lie groups and with
global objects like Drinfeld modules, Anderson's abelian $t$modules
and $t$motives, and Drinfeld shtukas. Moreover, we discuss the
existence of a Verschiebung map and apply it to deformations
of local shtukas and divisible local Anderson modules. As a tool
we use Faltings's and Abrashkin's theory of strict modules, which
we review to some extent.
Keywords:local shtuka, formal Drinfeld module, formal tmodule Categories:11G09, 13A35, 14L05 

9. CJM Online first
 Wang, Zhenjian

On algebraic surfaces associated with line arrangements
For a line arrangement $\mathcal{A}$ in the complex projective
plane $\mathbb{P}^2$, we investigate the compactification $\overline{F}$
in $\mathbb{P}^3$ of the affine Milnor fiber $F$ and its minimal
resolution $\widetilde{F}$. We compute the Chern numbers of $\widetilde{F}$
in terms of the combinatorics of the line arrangement $\mathcal{A}$.
As applications of the computation of the Chern numbers, we show
that the minimal resolution is never a quotient of a ball; in
addition, we also prove that $\widetilde{F}$ is of general type
when the arrangement has only nodes or triple points as singularities;
finally, we compute all the Hodge numbers of some $\widetilde{F}$
by using some knowledge about the Milnor fiber monodromy of the
arrangement.
Keywords:line arrangement, Milnor fiber, algebraic surface, Chern number Categories:32S22, 32S25, 14J17, 14J29, 14J70 

10. CJM 2018 (vol 70 pp. 1173)
 Viada, Evelina

An Explicit ManinDem'janenko Theorem in Elliptic Curves
Let $\mathcal{C}$ be a curve of genus at least $2$ embedded in $E_1
\times \cdots \times E_N$ where the $E_i$ are elliptic curves
for $i=1,\dots, N$. In this article we give an explicit sharp
bound for the NÃ©ronTate height of the points of $\mathcal{C}$ contained
in the union of all algebraic subgroups of dimension
$\lt \max(r_\mathcal{C}t_\mathcal{C},t_\mathcal{C})$
where $t_\mathcal{C}$, respectively $r_\mathcal{C}$, is the minimal dimension
of a translate, respectively of a torsion variety, containing
$\mathcal{C}$.
As a corollary, we give an explicit bound for the height of
the rational points of special curves, proving new cases of
the explicit Mordell Conjecture and in particular making explicit
(and slightly more general in the CM case) the ManinDem'janenko
method in products of elliptic curves.
Keywords:height, elliptic curve, explicit Mordell conjecture, explicit ManinDemjanenko theorem, rational points on a curve Categories:11G50, 14G40 

11. CJM 2018 (vol 70 pp. 1008)
 Elazar, Boaz; Shaviv, Ary

Schwartz Functions on Real Algebraic Varieties
We define Schwartz functions, tempered functions and tempered
distributions on (possibly singular) real algebraic varieties.
We prove that all classical properties of these spaces, defined
previously on affine spaces and on Nash manifolds, also hold
in the case of affine real algebraic varieties, and give partial
results for the nonaffine case.
Keywords:real algebraic geometry, Schwartz function, tempered distribution Categories:14P99, 14P05, 22E45, 46A11, 46F05 

12. CJM 2018 (vol 70 pp. 868)
 Ivorra, Florian; Yamazaki, Takao

Nori Motives of Curves with Modulus and Laumon $1$motives
Let $k$ be a number field. We describe the category of Laumon
$1$isomotives over $k$ as the universal category in the sense
of Nori associated with a quiver representation built out of
smooth proper $k$curves with two disjoint effective divisors
and a notion of $H^1_\mathrm{dR}$ for such "curves with modulus".
This result extends and relies on the theorem of J. Ayoub
and L. BarbieriViale that describes Deligne's category
of $1$isomotives in terms of Nori's Abelian category of motives.
Keywords:motive, curve with modulus, quiver representation Categories:19E15, 16G20, 14F42 

13. CJM 2018 (vol 70 pp. 628)
 Luo, Ye; Manjunath, Madhusudan

Smoothing of Limit Linear Series of Rank One on Saturated Metrized Complexes of Algebraic Curves
We investigate the smoothing problem of limit linear series of
rank one on an enrichment of the notions of nodal curves and
metrized complexes called saturated metrized complexes. We give
a finitely verifiable full criterion for smoothability of a limit
linear series of rank one on saturated metrized complexes, characterize
the space of all such smoothings, and extend the criterion to
metrized complexes. As applications, we prove that all limit
linear series of rank one are smoothable on saturated metrized
complexes corresponding to curves of compacttype, and prove
an analogue for saturated metrized complexes of a theorem of
Harris and Mumford on the characterization of nodal curves contained
in a given gonality stratum. In addition, we give a full combinatorial
criterion for smoothable limit linear series of rank one on saturated
metrized complexes corresponding to nodal curves whose dual graphs
are made of separate loops.
Keywords:limit linear series, metrized complex Category:14T05 

14. CJM 2017 (vol 70 pp. 1038)
 Elduque, Alberto

Order $3$ Elements in $G_2$ and Idempotents in Symmetric Composition Algebras
Order three elements in the exceptional groups of type $G_2$
are classified up to conjugation over arbitrary fields. Their
centralizers are computed, and the associated classification
of idempotents in symmetric composition algebras is obtained.
Idempotents have played a key role in the study and classification
of these algebras.
Over an algebraically closed field, there are two conjugacy classes
of order three elements in $G_2$ in characteristic not $3$ and
four of them in characteristic $3$. The centralizers in characteristic
$3$ fail to be smooth for one of these classes.
Keywords:symmetric composition algebra, Okubo algebra, automorphism group, centralizer, idempotent Categories:17A75, 14L15, 17B25, 20G15 

15. CJM 2017 (vol 70 pp. 451)
 Zhang, Chao

EkedahlOort strata for good reductions of Shimura varieties of Hodge type
For a Shimura variety of Hodge type with hyperspecial level
structure at a prime~$p$, Vasiu and Kisin constructed a smooth
integral model (namely the integral canonical model) uniquely
determined by a certain extension property. We define and study
the EkedahlOort stratifications on the special fibers of those
integral canonical models when $p\gt 2$. This generalizes
EkedahlOort stratifications defined and studied by Oort on moduli
spaces of principally polarized abelian varieties and those
defined and studied by Moonen, Wedhorn and Viehmann on good
reductions of Shimura varieties of PEL type. We show that the
EkedahlOort strata are parameterized by certain elements $w$ in
the Weyl group of the reductive group in the Shimura datum. We
prove that the stratum corresponding to $w$ is smooth of dimension
$l(w)$ (i.e. the length of $w$) if it is nonempty. We also
determine the closure of each stratum.
Keywords:Shimura variety, Fzip Categories:14G35, 11G18 

16. CJM 2017 (vol 70 pp. 481)
 Asakura, Masanori; Otsubo, Noriyuki

CM Periods, CM Regulators and Hypergeometric Functions, I
We prove the GrossDeligne conjecture on CM periods for motives
associated with $H^2$ of certain surfaces fibered over the projective
line. Then we prove for the same motives a formula which expresses
the $K_1$regulators in terms of hypergeometric functions ${}_3F_2$,
and obtain a new example of nontrivial regulators.
Keywords:period, regulator, complex multiplication, hypergeometric function Categories:14D07, 19F27, 33C20, 11G15, 14K22 

17. CJM 2017 (vol 70 pp. 702)
 Xia, Eugene Z.

The Algebraic de Rham Cohomology of Representation Varieties
The $\operatorname{SL}(2,\mathbb C)$representation varieties of punctured surfaces
form natural families parameterized by monodromies at the punctures.
In this paper, we compute the loci where these varieties are
singular for the cases of oneholed and twoholed tori and the
fourholed sphere. We then compute the de Rham cohomologies
of these varieties of the oneholed torus and the fourholed
sphere when the varieties are smooth via the Grothendieck theorem.
Furthermore, we produce the explicit GaussManin connection
on the natural family of the smooth $\operatorname{SL}(2,\mathbb C)$representation
varieties of the oneholed torus.
Keywords:surface, algebraic group, representation variety, de Rham cohomology Categories:14H10, 13D03, 14F40, 14H24, 14Q10, 14R20 

18. CJM 2017 (vol 70 pp. 354)
 Manon, Christopher

Toric geometry of $SL_2(\mathbb{C})$ free group character varieties from outer space
Culler and Vogtmann defined a simplicial space $O(g)$ called
outer space to study the outer automorphism group
of the free group $F_g$. Using representation theoretic methods,
we give an embedding of $O(g)$ into the analytification of $\mathcal{X}(F_g,
SL_2(\mathbb{C})),$ the $SL_2(\mathbb{C})$ character variety
of $F_g,$ reproving a result of Morgan and Shalen. Then we show
that every point $v$ contained in a maximal cell of $O(g)$ defines
a flat degeneration of $\mathcal{X}(F_g, SL_2(\mathbb{C}))$ to
a toric variety $X(P_{\Gamma})$. We relate $\mathcal{X}(F_g,
SL_2(\mathbb{C}))$ and $X(v)$ topologically by showing that there
is a surjective, continuous, proper map $\Xi_v: \mathcal{X}(F_g,
SL_2(\mathbb{C})) \to X(v)$. We then show that this map is a
symplectomorphism on a dense, open subset of $\mathcal{X}(F_g,
SL_2(\mathbb{C}))$ with respect to natural symplectic structures
on $\mathcal{X}(F_g, SL_2(\mathbb{C}))$ and $X(v)$. In this
way, we construct an integrable Hamiltonian system in $\mathcal{X}(F_g,
SL_2(\mathbb{C}))$ for each point in a maximal cell of $O(g)$,
and we show that each $v$ defines a topological decomposition
of $\mathcal{X}(F_g, SL_2(\mathbb{C}))$ derived from the decomposition
of $X(P_{\Gamma})$ by its torus orbits. Finally, we show that
the valuations coming from the closure of a maximal cell in $O(g)$
all arise as divisorial valuations built from an associated projective
compactification of $\mathcal{X}(F_g, SL_2(\mathbb{C})).$
Keywords:character variety, outer space, analytification, compactification, integrable system Categories:14M25, 14T05, 14D20 

19. CJM 2016 (vol 69 pp. 1274)
 Favacchio, Giuseppe; Guardo, Elena

The Minimal Free Resolution of Fat Almost Complete Intersections in $\mathbb{P}^1\times \mathbb{P}^1$
A current research theme is to compare symbolic powers of an
ideal
$I$ with the regular powers of $I$. In this paper, we focus on
the
case that $I=I_X$ is an ideal defining an almost complete
intersection (ACI) set of points $X$ in
$\mathbb{P}^1 \times \mathbb{P}^1$.
In particular,
we describe a minimal free bigraded resolution of a non
arithmetically CohenMacaulay (also non homogeneous) set $\mathcal
Z$ of fat
points whose support is an ACI, generalizing
a result of S. Cooper et al.
for homogeneous sets of triple points. We call
$\mathcal Z$ a fat ACI. We also show that its symbolic and ordinary
powers are equal, i.e,
$I_{\mathcal Z}^{(m)}=I_{\mathcal Z}^{m}$ for any $m\geq 1.$
Keywords:points in $\mathbb{P}^1\times \mathbb{P}^1$, symbolic powers, resolution, arithmetically CohenMacaulay Categories:13C40, 13F20, 13A15, 14C20, 14M05 

20. CJM 2016 (vol 69 pp. 767)
 Choi, Suyoung; Park, Hanchul

Wedge Operations and Torus Symmetries II
A fundamental idea in toric topology is that classes of manifolds
with wellbehaved torus actions (simply, toric spaces) are classified
by pairs of simplicial complexes and (nonsingular) characteristic
maps. The authors in their previous paper provided a new way
to find all characteristic maps on a simplicial complex $K(J)$
obtainable by a sequence of wedgings from $K$. The main idea
was that characteristic maps on $K$ theoretically determine all
possible characteristic maps on a wedge of $K$.
In this work, we further develop our previous work for classification
of toric spaces. For a starshaped simplicial sphere $K$ of dimension
$n1$ with $m$ vertices, the Picard number $\operatorname{Pic}(K)$ of $K$ is
$mn$. We refer to $K$ as a seed if $K$ cannot be obtained
by wedgings. First, we show that, for a fixed positive integer
$\ell$, there are at most finitely many seeds of Picard number
$\ell$ supporting characteristic maps. As a corollary, the conjecture
proposed by V.V. Batyrev in 1991 is solved affirmatively.
Second, we investigate a systematic method to find all characteristic
maps on $K(J)$ using combinatorial objects called (realizable)
puzzles that only depend on a seed $K$.
These two facts lead to a practical way to classify the toric
spaces of fixed Picard number.
Keywords:puzzle, toric variety, simplicial wedge, characteristic map Categories:57S25, 14M25, 52B11, 13F55, 18A10 

21. CJM 2016 (vol 68 pp. 1362)
 Papikian, Mihran; Rabinoff, Joseph

Optimal Quotients of Jacobians with Toric Reduction and Component Groups
Let $J$ be a Jacobian variety with toric reduction
over a local field $K$.
Let $J \to E$ be an optimal quotient defined over $K$, where
$E$ is an elliptic curve.
We give examples in which the functorially induced map $\Phi_J
\to \Phi_E$
on component groups of the NÃ©ron models is not surjective.
This answers a question of Ribet and Takahashi.
We also give various criteria under which $\Phi_J \to \Phi_E$
is surjective, and discuss
when these criteria hold for the Jacobians of modular curves.
Keywords:Jacobians with toric reduction, component groups, modular curves Categories:11G18, 14G22, 14G20 

22. CJM 2016 (vol 69 pp. 143)
 Levinson, Jake

Onedimensional Schubert Problems with Respect to Osculating Flags
We consider Schubert problems with respect to flags osculating
the rational normal curve. These problems are of special interest
when the osculation points are all real  in this case, for
zerodimensional Schubert problems, the solutions are "as real
as possible". Recent work by Speyer has extended the theory
to the moduli space
$
\overline{\mathcal{M}_{0,r}}
$,
allowing the points to collide.
These give rise to smooth covers of
$
\overline{\mathcal{M}_{0,r}}
(\mathbb{R})
$, with structure
and monodromy described by Young tableaux and jeu de taquin.
In this paper, we give analogous results on onedimensional Schubert
problems over
$
\overline{\mathcal{M}_{0,r}}
$.
Their (real) geometry turns out to
be described by orbits of SchÃ¼tzenberger promotion and a
related operation involving tableau evacuation. Over
$\mathcal{M}_{0,r}$,
our results show that the real points of the solution curves
are smooth.
We also find a new identity involving "firstorder" Ktheoretic
LittlewoodRichardson coefficients, for which there does not
appear to be a known combinatorial proof.
Keywords:Schubert calculus, stable curves, ShapiroShapiro Conjecture, jeu de taquin, growth diagram, promotion Categories:14N15, 05E99 

23. CJM 2016 (vol 68 pp. 1096)
 Smith, Benjamin H.

Singular $G$Monopoles on $S^1\times \Sigma$
This article provides an account of the functorial correspondence
between irreducible singular $G$monopoles on $S^1\times \Sigma$
and $\vec{t}$stable meromorphic pairs on $\Sigma$.
A theorem of B. Charbonneau and J. Hurtubise
is thus generalized here from unitary to arbitrary
compact, connected gauge groups. The required distinctions and
similarities for unitary versus arbitrary gauge are clearly outlined
and many parallels are drawn for easy transition. Once the correspondence
theorem is complete, the spectral decomposition is addressed.
Keywords:connection, curvature, instanton, monopole, stability, Bogomolny equation, Sasakian geometry, cameral covers Categories:53C07, 14D20 

24. CJM 2016 (vol 68 pp. 784)
 Doran, Charles F.; Harder, Andrew

Toric Degenerations and Laurent Polynomials Related to Givental's LandauGinzburg Models
For an appropriate class of Fano complete intersections in toric
varieties, we prove that there is a concrete relationship between
degenerations to specific toric subvarieties and expressions
for Givental's LandauGinzburg models as Laurent polynomials.
As a result, we show that Fano varieties presented as complete
intersections in partial flag manifolds admit degenerations to
Gorenstein toric weak Fano varieties, and their Givental LandauGinzburg
models can be expressed as corresponding Laurent polynomials.
We also use this to show that all of the Laurent polynomials
obtained by Coates, Kasprzyk and Prince by the so called Przyjalkowski
method correspond to toric degenerations of the corresponding
Fano variety. We discuss applications to geometric transitions
of CalabiYau varieties.
Keywords:Fano varieties, LandauGinzburg models, CalabiYau varieties, toric varieties Categories:14M25, 14J32, 14J33, 14J45 

25. CJM 2016 (vol 69 pp. 613)
 Moon, HanBom

Mori's Program for $\overline{M}_{0,7}$ with Symmetric Divisors
We complete Mori's program with symmetric divisors for the moduli
space of stable sevenpointed rational curves. We describe all
birational models in terms of explicit blowups and blowdowns.
We also give a moduli theoretic description of the first flip,
which has not appeared in the literature.
Keywords:moduli of curves, minimal model program, Mori dream space Categories:14H10, 14E30 
