1. CJM Online first
 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 

2. CJM Online first
 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 

3. CJM Online first
 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 

4. CJM Online first
 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 

5. CJM Online first
 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 

6. 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 

7. 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 

8. 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 

9. 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 

10. CJM Online first
 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 

11. CJM 2016 (vol 69 pp. 338)
 Garbagnati, Alice

On K3 Surface Quotients of K3 or Abelian Surfaces
The aim of this paper is to prove that a K3 surface is the minimal
model of the quotient of an Abelian surface by a group $G$ (respectively
of a K3 surface by an Abelian group $G$) if and only if a certain
lattice is primitively embedded in its NÃ©ronSeveri group.
This allows one to describe the coarse moduli space of the K3
surfaces which are (rationally) $G$covered by Abelian or K3
surfaces (in the latter case $G$ is an Abelian group).
If either $G$ has order 2 or $G$ is cyclic and acts on an Abelian
surface, this result was already known, so we extend it to the
other cases.
Moreover, we prove that a K3 surface $X_G$ is the minimal model
of the quotient of an Abelian surface by a group $G$ if and only
if a certain configuration of rational curves is present on $X_G$.
Again this result was known only in some special cases, in particular
if $G$ has order 2 or 3.
Keywords:K3 surfaces, Kummer surfaces, Kummer type lattice, quotient surfaces Categories:14J28, 14J50, 14J10 

12. CJM 2016 (vol 68 pp. 541)
 GarciaArmas, Mario

Strongly Incompressible Curves
Let $G$ be a finite group. A faithful $G$variety $X$ is called
strongly incompressible if every dominant $G$equivariant rational
map of $X$ onto another faithful $G$variety $Y$ is birational.
We settle the problem of existence of strongly incompressible
$G$curves for any finite group $G$ and any base field $k$ of
characteristic zero.
Keywords:algebraic curves, group actions, Galois cohomology Categories:14L30, 14E07, 14H37 

13. CJM 2016 (vol 68 pp. 504)
14. CJM 2016 (vol 68 pp. 361)
 Fité, Francesc; González, Josep; Lario, Joan Carles

Frobenius Distribution for Quotients of Fermat Curves of Prime Exponent
Let $\mathcal{C}$ denote the Fermat curve over $\mathbb{Q}$ of prime
exponent $\ell$. The Jacobian $\operatorname{Jac}(\mathcal{C})$
of~$\mathcal{C}$ splits over $\mathbb{Q}$ as the product of Jacobians
$\operatorname{Jac}(\mathcal{C}_k)$, $1\leq k\leq \ell2$, where
$\mathcal{C}_k$ are curves obtained as quotients of $\mathcal{C}$ by
certain subgroups of automorphisms of $\mathcal{C}$. It is well known
that $\operatorname{Jac}(\mathcal{C}_k)$ is the power of an absolutely
simple abelian variety $B_k$ with complex multiplication. We call
degenerate those pairs $(\ell,k)$ for which $B_k$ has degenerate CM
type. For a nondegenerate pair $(\ell,k)$, we compute the SatoTate
group of $\operatorname{Jac}(\mathcal{C}_k)$, prove the generalized
SatoTate Conjecture for it, and give an explicit method to compute
the moments and measures of the involved distributions. Regardless of
$(\ell,k)$ being degenerate or not, we also obtain Frobenius
equidistribution results for primes of certain residue degrees in the
$\ell$th cyclotomic field. Key to our results is a detailed study of
the rank of certain generalized Demjanenko matrices.
Keywords:SatoTate group, Fermat curve, Frobenius distribution Categories:11D41, 11M50, 11G10, 14G10 

15. CJM 2016 (vol 68 pp. 280)
 da Silva, Genival; Kerr, Matt; Pearlstein, Gregory

Arithmetic of Degenerating Principal Variations of Hodge Structure: Examples Arising from Mirror Symmetry and Middle Convolution
We collect evidence in support of a conjecture of Griffiths,
Green
and Kerr
on the arithmetic of extension classes of
limiting
mixed Hodge structures arising from semistable degenerations
over
a number field. After briefly summarizing how a result of Iritani
implies this conjecture for a collection of hypergeometric
CalabiYau threefold examples studied by Doran and Morgan,
the authors investigate a sequence of (nonhypergeometric) examples
in dimensions $1\leq d\leq6$ arising from Katz's theory of the
middle
convolution.
A crucial role is played by the MumfordTate
group (which is $G_{2}$) of the family of 6folds, and the theory
of boundary components of MumfordTate domains.
Keywords:variation of Hodge structure, limiting mixed Hodge structure, CalabiYau variety, middle convolution, MumfordTate group Categories:14D07, 14M17, 17B45, 20G99, 32M10, 32G20 

16. CJM 2015 (vol 68 pp. 241)
 Allermann, Lars; Hampe, Simon; Rau, Johannes

On Rational Equivalence in Tropical Geometry
This article discusses the concept of rational equivalence
in tropical
geometry
(and replaces an older and imperfect version).
We give the basic definitions in the context of tropical varieties
without boundary points and prove some basic properties.
We then compute the ``bounded'' Chow groups of $\mathbb{R}^n$ by showing
that they are isomorphic
to the group of fan cycles. The main step in the proof is of
independent interest:
We show that every tropical cycle in $\mathbb{R}^n$ is a sum of (translated)
fan cycles. This also
proves that the intersection ring of tropical cycles is generated
in codimension 1 (by hypersurfaces).
Keywords:tropical geometry, rational equivalence Category:14T05 

17. CJM 2015 (vol 68 pp. 67)
18. CJM 2015 (vol 68 pp. 334)
 Demchenko, Oleg; Gurevich, Alexander

Kernels in the Category of Formal Group Laws
Fontaine described the category of formal groups over the ring
of Witt vectors over a finite field
of characteristic $p$ with the aid of triples consisting of the
module of logarithms,
the DieudonnÃ© module and the morphism from the former to the
latter. We propose
an explicit construction for the kernels in this category in
term of Fontaine's triples.
The construction is applied to the formal norm homomorphism in
the case of an unramified extension
of $\mathbb{Q}_p$ and of a totally ramified extension of degree less
or equal than $p$. A similar
consideration applied to a global extension allows us to establish
the existence of a strict
isomorphism between the formal norm torus and a formal group
law coming from $L$series.
Keywords:formal groups, $p$divisible groups, Dieudonne modules, norm tori Category:14L05 

19. CJM 2015 (vol 67 pp. 961)
 Abuaf, Roland; Boralevi, Ada

Orthogonal Bundles and SkewHamiltonian Matrices
Using properties of skewHamiltonian matrices and classic
connectedness results, we prove that the moduli space
$M_{ort}^0(r,n)$ of stable rank $r$ orthogonal vector bundles
on $\mathbb{P}^2$, with Chern classes $(c_1,c_2)=(0,n)$, and trivial
splitting on the general line, is smooth irreducible of
dimension $(r2)n\binom{r}{2}$ for $r=n$ and $n \ge 4$, and
$r=n1$ and $n\ge 8$. We speculate that the result holds in
greater generality.
Keywords:orthogonal vector bundles, moduli spaces, skewHamiltonian matrices Categories:14J60, 15B99 

20. CJM 2015 (vol 67 pp. 1201)
 Aluffi, Paolo; Faber, Eleonore

Chern Classes of Splayed Intersections
We generalize the Chern class relation for the transversal intersection
of two nonsingular
varieties to a relation for possibly singular varieties, under
a splayedness assumption.
We show that the relation for the ChernSchwartzMacPherson classes
holds for two splayed hypersurfaces in a nonsingular variety,
and under a `strong splayedness' assumption for more
general subschemes. Moreover, the relation is shown to hold for
the ChernFulton classes
of any two splayed subschemes.
The main tool is a formula for Segre classes of splayed
subschemes. We also discuss the Chern class relation under the
assumption that one of the
varieties is a general very ample divisor.
Keywords:splayed intersection, ChernSchwartzMacPherson class, ChernFulton class, splayed blowup, Segre class Categories:14C17, 14J17 

21. CJM 2015 (vol 67 pp. 1109)
 Nohara, Yuichi; Ueda, Kazushi

Goldman Systems and Bending Systems
We show that the moduli space
of parabolic bundles on the projective line
and the polygon space are isomorphic,
both as complex manifolds
and symplectic manifolds equipped with structures of completely integrable systems,
if the stability parameters are
small.
Keywords:toric degeneration Categories:53D30, 14H60 

22. CJM 2015 (vol 68 pp. 24)
 Bonfanti, Matteo Alfonso; van Geemen, Bert

Abelian Surfaces with an Automorphism and Quaternionic Multiplication
We construct one dimensional families of Abelian surfaces with
quaternionic multiplication
which also have an automorphism of order three or four. Using Barth's
description of the moduli space of $(2,4)$polarized Abelian surfaces,
we find the Shimura curve parametrizing these Abelian surfaces in a
specific case.
We explicitly relate these surfaces to the Jacobians of genus two
curves studied by Hashimoto and Murabayashi.
We also describe a (Humbert) surface in Barth's moduli space which
parametrizes Abelian surfaces with real multiplication by
$\mathbf{Z}[\sqrt{2}]$.
Keywords:abelian surfaces, moduli, shimura curves Categories:14K10, 11G10, 14K20 

23. CJM 2015 (vol 67 pp. 696)
 Zhang, Tong

Geography of Irregular Gorenstein 3folds
In this paper, we study the explicit geography problem of irregular Gorenstein minimal 3folds of general type. We generalize the classical NoetherCastelnuovo type inequalities for irregular surfaces to irregular 3folds according to the Albanese dimension.
Keywords:3fold, geography, irregular variety Category:14J30 

24. CJM 2014 (vol 67 pp. 923)
 Pan, Ivan Edgardo; Simis, Aron

Cremona Maps of de JonquiÃ¨res Type
This paper is concerned with suitable generalizations of a plane de
JonquiÃ¨res map to higher dimensional space
$\mathbb{P}^n$ with $n\geq 3$.
For each given point of $\mathbb{P}^n$ there is a subgroup of the entire
Cremona group of dimension $n$
consisting of such maps.
One studies both geometric and grouptheoretical properties of this notion.
In the case where $n=3$ one describes an explicit set of generators of
the group and gives a homological characterization
of a basic subgroup thereof.
Keywords:Cremona map, de JonquiÃ¨res map, Cremona group, minimal free resolution Categories:14E05, 13D02, 13H10, 14E07, 14M05, 14M25 

25. CJM 2014 (vol 67 pp. 527)
 Brugallé, Erwan; Shaw, Kristin

Obstructions to Approximating Tropical Curves in Surfaces Via Intersection Theory
We provide some new local obstructions to
approximating
tropical curves in
smooth tropical surfaces. These obstructions are based on
a
relation between tropical and complex intersection theories which is
also established here. We give
two applications of the methods developed in this paper.
First we classify all locally irreducible approximable 3valent fan tropical
curves in a
fan tropical plane.
Secondly, we prove that a generic nonsingular
tropical surface
in tropical projective 3space contains finitely
many approximable tropical lines
if
it is of degree 3, and contains no approximable tropical lines if
it is of degree 4 or more.
Keywords:tropical geometry, amoebas, approximation of tropical varieties, intersection theory Categories:14T05, 14M25 
