1. CJM Online first
 MirandaNeto, Cleto B.

On special fiber rings of modules
We prove results concerning the multiplicity as well as the CohenMacaulay
and Gorenstein properties of the special fiber ring $\mathscr{F}(E)$
of a finitely generated $R$module $E\subsetneq R^e$ over a Noetherian
local ring $R$ with infinite residue field. Assuming that $R$
is CohenMacaulay of dimension $1$ and that $E$ has finite colength
in $R^e$, our main result establishes an asymptotic length formula
for the multiplicity of $\mathscr{F}(E)$, which, in addition to being
of independent interest, allows us to derive a CohenMacaulayness
criterion and to detect a curious relation to the BuchsbaumRim
multiplicity of $E$ in this setting. Further, we provide a Gorensteinness
characterization for $\mathscr{F}(E)$ in the more general situation where
$R$ is CohenMacaulay of arbitrary dimension and $E$ is not necessarily
of finite colength, and we notice a constraint in terms of the
second analytic deviation of the module $E$ if its reduction
number is at least three.
Keywords:special fiber ring, Rees algebra, reduction, reduction number, analytic spread, HilbertSamuel multiplicity, CohenMacaulay, Gorenstein, BuchsbaumRim multiplicity Categories:13A30, 13H10, 13H15, 13A02, 13C15, 13D40, , 13E15 

2. 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 

3. 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 

4. 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 

5. CJM Online first
 Galetto, Federico; Geramita, Anthony Vito; Wehlau, David Louis

Degrees of regular sequences with a symmetric group action
We consider ideals in a polynomial ring that are generated by regular sequences of homogeneous polynomials and are stable under the action of the symmetric group permuting the variables. In previous work, we determined the possible isomorphism types for these ideals. Following up on that work, we now analyze the possible degrees of the elements in such regular sequences. For each case of our classification, we provide some criteria guaranteeing the existence of regular sequences in certain degrees.
Keywords:Complete intersection, symmetric group, regular sequences Categories:13A02, 13A50, 20C30 

6. CJM Online first
 Geroldinger, Alfred; Zhong, Qinghai

Long sets of lengths with maximal elasticity
We introduce a new invariant describing the structure of sets of lengths in atomic monoids and domains. For an atomic monoid $H$, let $\Delta_{\rho} (H)$ be the set of all positive integers $d$ which occur as differences of arbitrarily long arithmetical progressions contained in sets of lengths having maximal elasticity $\rho (H)$. We study $\Delta_{\rho} (H)$ for transfer Krull monoids of finite type (including commutative Krull domains with finite class group) with methods from additive combinatorics, and also for a class of weakly Krull domains (including orders in algebraic number fields) for which we use ideal theoretic methods.
Keywords:transfer Krull monoid, weakly Krull monoid, set of length, elasticity Categories:13A05, 13F05, 16H10, 16U30, 20M13 

7. CJM 2017 (vol 69 pp. 992)
 Bremner, Murray; Dotsenko, Vladimir

Classification of Regular Parametrized Onerelation Operads
JeanLouis Loday introduced a class of symmetric operads generated
by one bilinear operation subject to one
relation making each leftnormed product of three elements equal
to a linear combination
of rightnormed products:
\[
(a_1a_2)a_3=\sum_{\sigma\in S_3}x_\sigma\, a_{\sigma(1)}(a_{\sigma(2)}a_{\sigma(3)})\
;
\]
such an operad is called a parametrized onerelation operad.
For a particular choice of parameters $\{x_\sigma\}$,
this operad is said to be regular if each of its components is
the regular representation of the symmetric group; equivalently, the corresponding free algebra on a vector space $V$ is, as a
graded vector space, isomorphic to the tensor
algebra of $V$. We classify, over an algebraically closed field
of characteristic zero, all regular parametrized onerelation
operads.
In fact, we prove that each such operad is isomorphic to one
of the following five operads: the leftnilpotent operad
defined by the relation $((a_1a_2)a_3)=0$, the associative operad,
the Leibniz operad, the dual Leibniz (Zinbiel) operad, and the
Poisson operad.
Our computational methods combine linear algebra over polynomial
rings, representation theory of the symmetric group, and
GrÃ¶bner bases for determinantal ideals and their radicals.
Keywords:parametrized onerelation algebra, algebraic operad, Koszul duality, representation theory of the symmetric group, determinantal ideal, GrÃ¶bner basis Categories:18D50, 13B25, 13P10, 13P15, 15A54, 1704, , , , , 17A30, 17A50, 20C30, 68W30 

8. 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 

9. 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 

10. 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 

11. CJM 2016 (vol 69 pp. 241)
 Adamus, Janusz; Seyedinejad, Hadi

Finite Determinacy and Stability of Flatness of Analytic Mappings
It is proved that flatness of an analytic mapping germ from a
complete intersection is determined by its sufficiently high
jet. As a consequence, one obtains finite determinacy of complete
intersections. It is also shown that flatness and openness are
stable under deformations.
Keywords:finite determinacy, stability, flatness, openness, complete intersection Categories:58K40, 58K25, 32S05, 58K20, 32S30, 32B99, 32C05, 13B40 

12. 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 

13. CJM 2014 (vol 67 pp. 1024)
 Ashraf, Samia; Azam, Haniya; Berceanu, Barbu

Representation Stability of Power Sets and Square Free Polynomials
The symmetric group $\mathcal{S}_n$ acts on the power
set $\mathcal{P}(n)$ and also on the set of
square free polynomials in $n$ variables. These
two related representations are analyzed from the stability point
of view. An application is given for the action of the symmetric
group on the cohomology of the pure braid group.
Keywords:symmetric group modules, square free polynomials, representation stability, Arnold algebra Categories:20C30, 13A50, 20F36, 55R80 

14. CJM 2013 (vol 66 pp. 1225)
15. CJM 2012 (vol 66 pp. 3)
 Abdesselam, Abdelmalek; Chipalkatti, Jaydeep

On Hilbert Covariants
Let $F$ denote a binary form of order $d$ over the
complex numbers. If $r$ is a divisor of $d$, then the Hilbert covariant
$\mathcal{H}_{r,d}(F)$ vanishes exactly when $F$ is the perfect power of an
order $r$ form. In geometric terms, the coefficients of $\mathcal{H}$ give
defining equations for the image variety $X$ of an embedding $\mathbf{P}^r
\hookrightarrow \mathbf{P}^d$. In this paper we describe a new construction of
the Hilbert covariant; and simultaneously situate it into a wider class of
covariants called the GÃ¶ttingen covariants, all of which vanish on
$X$. We prove that the ideal generated by the coefficients of $\mathcal{H}$
defines $X$ as a scheme. Finally, we exhibit a generalisation of the
GÃ¶ttingen covariants to $n$ary forms using the classical Clebsch transfer principle.
Keywords:binary forms, covariants, $SL_2$representations Categories:14L30, 13A50 

16. CJM 2012 (vol 65 pp. 823)
 Guardo, Elena; Harbourne, Brian; Van Tuyl, Adam

Symbolic Powers Versus Regular Powers of Ideals of General Points in $\mathbb{P}^1 \times \mathbb{P}^1$
Recent work of EinLazarsfeldSmith and HochsterHuneke
raised the problem of which symbolic powers of an ideal
are contained in a given ordinary power of the ideal.
BocciHarbourne developed methods to address this problem,
which involve asymptotic numerical characters of
symbolic powers of the ideals. Most of the work
done up to now has been done for ideals defining 0dimensional
subschemes of projective space.
Here we focus on certain subschemes given by
a union of lines in $\mathbb{P}^3$ which can also be viewed
as points in $\mathbb{P}^1 \times \mathbb{P}^1$.
We also obtain results on the
closely related problem, studied by Hochster and by LiSwanson, of
determining situations for which
each symbolic power of an ideal is an ordinary power.
Keywords:symbolic powers, multigraded, points Categories:13F20, 13A15, 14C20 

17. CJM 2012 (vol 65 pp. 634)
 Mezzetti, Emilia; MiróRoig, Rosa M.; Ottaviani, Giorgio

Laplace Equations and the Weak Lefschetz Property
We prove that $r$ independent homogeneous polynomials of the same degree $d$
become dependent when restricted to any hyperplane if and only if their inverse system parameterizes a variety
whose $(d1)$osculating spaces have dimension smaller than expected. This gives an equivalence
between an algebraic notion (called Weak Lefschetz Property)
and a differential geometric notion, concerning varieties which satisfy certain Laplace equations. In the toric case,
some relevant examples are classified and as byproduct we provide counterexamples to Ilardi's conjecture.
Keywords:osculating space, weak Lefschetz property, Laplace equations, toric threefold Categories:13E10, 14M25, 14N05, 14N15, 53A20 

18. CJM 2010 (vol 62 pp. 1131)
 Kleppe, Jan O.

Moduli Spaces of Reflexive Sheaves of Rank 2
Let $\mathcal{F}$ be a coherent rank $2$ sheaf on a scheme $Y \subset \mathbb{P}^{n}$ of
dimension at least two and let $X \subset Y$ be the zero set of a section
$\sigma \in H^0(\mathcal{F})$. In this paper, we study the relationship between the
functor that deforms the pair $(\mathcal{F},\sigma)$ and the two functors that deform
$\mathcal{F}$ on $Y$, and $X$ in $Y$, respectively. By imposing some conditions on two
forgetful maps between the functors, we prove that the scheme structure of
\emph{e.g.,} the moduli scheme ${\rm M_Y}(P)$ of stable sheaves on a threefold $Y$
at $(\mathcal{F})$, and the scheme structure at $(X)$ of the Hilbert scheme of curves
on $Y$ become closely related. Using this relationship, we get criteria for the
dimension and smoothness of $ {\rm M_{Y}}(P)$ at $(\mathcal{F})$, without assuming $
{\textrm{Ext}^2}(\mathcal{F} ,\mathcal{F} ) = 0$. For reflexive sheaves on $Y=\mathbb{P}^{3}$ whose
deficiency module $M = H_{*}^1(\mathcal{F})$ satisfies $ {_{0}\! \textrm{Ext}^2}(M ,M ) = 0 $
(\emph{e.g.,} of diameter at most 2),
we get necessary and sufficient conditions of unobstructedness that coincide
in the diameter one case. The conditions are further equivalent to the
vanishing of certain graded Betti numbers of the free graded minimal
resolution of $H_{*}^0(\mathcal{F})$. Moreover, we show that every irreducible
component of ${\rm M}_{\mathbb{P}^{3}}(P)$ containing a reflexive sheaf of diameter
one is reduced (generically smooth) and we compute its dimension. We also
determine a good lower bound for the dimension of any component of ${\rm
M}_{\mathbb{P}^{3}}(P)$ that contains a reflexive stable sheaf with ``small''
deficiency module $M$.
Keywords:moduli space, reflexive sheaf, Hilbert scheme, space curve, Buchsbaum sheaf, unobstructedness, cup product, graded Betti numbers.xdvi Categories:14C05, qqqqq14D22, 14F05, 14J10, 14H50, 14B10, 13D02, 13D07 

19. CJM 2009 (vol 62 pp. 721)
 Boocher, Adam; Daub, Michael; Johnson, Ryan K.; Lindo, H.; Loepp, S.; Woodard, Paul A.

Formal Fibers of Unique Factorization Domains
Let $(T,M)$ be a complete local (Noetherian) ring such that $\dim T\geq 2$ and
$T=T/M$ and let $\{p_i\} _{i \in \mathcal I}$ be a collection of
elements of T indexed by a set $\mathcal I$ so that $\mathcal I  < T$.
For each $i \in \mathcal{I}$, let $C_i$:={$Q_{i1}$,$\dots$,$Q_{in_i}$}
be a set of nonmaximal prime ideals containing $p_i$ such that the $Q_{ij}$
are incomparable and $p_i\in Q_{jk}$ if and only if $i=j$. We provide necessary
and sufficient conditions so that T is the ${\bf m}$adic completion of a local unique
factorization domain $(A, {\bf m})$, and for each $i \in \mathcal I$, there exists a unit
$t_i$ of T so that $p_{i}t_i \in A$ and $C_i$
is the set of prime ideals $Q$ of $T$ that are maximal with respect to the condition
that $Q \cap A = p_{i}t_{i}A$.
We then use this result to construct a
(nonexcellent) unique factorization domain containing many ideals for which tight closure and
completion do not commute. As another application, we construct a unique factorization
domain A most of whose formal fibers are geometrically regular.
Categories:13J10, 13J05 

20. CJM 2009 (vol 61 pp. 888)
 Novik, Isabella; Swartz, Ed

Face Ring Multiplicity via CMConnectivity Sequences
The multiplicity conjecture of Herzog, Huneke, and Srinivasan
is verified for the face rings of the following classes of
simplicial complexes: matroid complexes, complexes of dimension
one and two,
and Gorenstein complexes of dimension at most four.
The lower bound part of this conjecture is also established for the
face rings of all doubly CohenMacaulay complexes whose 1skeleton's
connectivity does not exceed the codimension plus one as well as for
all $(d1)$dimensional $d$CohenMacaulay complexes.
The main ingredient of the proofs is a new interpretation
of the minimal shifts in the resolution of the face ring
$\field[\Delta]$ via the CohenMacaulay connectivity of the
skeletons of $\Delta$.
Categories:13F55, 52B05;, 13H15;, 13D02;, 05B35 

21. CJM 2009 (vol 61 pp. 950)
 Tange, Rudolf

Infinitesimal Invariants in a Function Algebra
Let $G$ be a reductive connected linear algebraic group
over an algebraically closed field of positive
characteristic and let $\g$ be its Lie algebra.
First we extend a wellknown result about the Picard group of a
semisimple group to reductive groups.
Then we prove that if the derived group is simply connected
and $\g$ satisfies a
mild condition, the algebra $K[G]^\g$ of regular functions
on $G$ that are invariant under the action of $\g$ derived
from the conjugation action is a unique factorisation domain.
Categories:20G15, 13F15 

22. CJM 2009 (vol 61 pp. 930)
 Sidman, Jessica; Sullivant, Seth

Prolongations and Computational Algebra
We explore the geometric notion of prolongations in the setting of
computational algebra, extending results of Landsberg and Manivel
which relate prolongations to equations for secant varieties. We also
develop methods for computing prolongations that are combinatorial in
nature. As an application, we use prolongations to derive a new
family of secant equations for the binary symmetric model in
phylogenetics.
Categories:13P10, 14M99 

23. CJM 2009 (vol 61 pp. 762)
24. CJM 2009 (vol 61 pp. 205)
 Marshall, M.

Representations of NonNegative Polynomials, Degree Bounds and Applications to Optimization
Natural sufficient conditions for a polynomial to have a local minimum
at a point are considered. These conditions tend to hold with
probability $1$. It is shown that polynomials satisfying these
conditions at each minimum point have nice presentations in terms of
sums of squares. Applications are given to optimization on a compact
set and also to global optimization. In many cases, there are degree
bounds for such presentations. These bounds are of theoretical
interest, but they appear to be too large to be of much practical use
at present. In the final section, other more concrete degree bounds
are obtained which ensure at least that the feasible set of solutions
is not empty.
Categories:13J30, 12Y05, 13P99, 14P10, 90C22 

25. CJM 2009 (vol 61 pp. 29)
 Casanellas, M.

The Minimal Resolution Conjecture for Points on the Cubic Surface
In this paper we prove that a generalized version of the Minimal
Resolution Conjecture given by Musta\c{t}\v{a} holds for certain
general sets of points on a smooth cubic surface $X \subset
\PP^3$. The main tool used is Gorenstein liaison theory and, more
precisely, the relationship between the free resolutions of two linked schemes.
Categories:13D02, 13C40, 14M05, 14M07 
