Characteristic cycles and Gevrey series solutions of AA-hypergeometric systems

We compute the $L$-characteristic cycle of an $A$-hypergeometric system and higher Euler-Koszul homology modules of the toric ring. We also prove upper semicontinuity results about the multiplicities in these cycles and apply our results to analyze the behavior of Gevrey solution spaces of the system.Comment: 22 page

An Array of Disjoint Maximal Constant Weight Codes

We show that when gcd(n,w) = 1, the set of binary words of length n and weight w can be partitioned to give n maximal w-weight codes. It follows that under the same hypothesis, the least cardinal of a maximal constant weight code is at most 1/n times n choose w

Poset structures in Boij-S\"oderberg theory

Boij-S\"oderberg theory is the study of two cones: the cone of cohomology tables of coherent sheaves over projective space and the cone of standard graded minimal free resolutions over a polynomial ring. Each cone has a simplicial fan structure induced by a partial order on its extremal rays. We provide a new interpretation of these partial orders in terms of the existence of nonzero homomorphisms, for both the general and the equivariant constructions. These results provide new insights into the families of sheaves and modules at the heart of Boij-S\"oderberg theory: supernatural sheaves and Cohen-Macaulay modules with pure resolutions. In addition, our results strongly suggest the naturality of these partial orders, and they provide tools for extending Boij-S\"oderberg theory to other graded rings and projective varieties.Comment: 23 pages; v2: Added Section 8, reordered previous section

Systems of parameters and holonomicity of A-hypergeometric systems

The main result is an elementary proof of holonomicity for A-hypergeometric systems, with no requirements on the behavior of their singularities, originally due to Adolphson [Ado94] after the regular singular case by Gelfand and Gelfand [GG86]. Our method yields a direct de novo proof that A-hypergeometric systems form holonomic families over their parameter spaces, as shown by Matusevich, Miller, and Walther [MMW05]

A-graded methods for monomial ideals

We use \ZZ^d-gradings to study d-dimensional monomial ideals. The Koszul functor is employed to interpret the quasidegrees of local cohomology in terms of the geometry of distractions and to explicitly compute the multiplicities of exponents. These multigraded techniques originate from the study of hypergeometric systems of differential equations.Comment: Reorganized version with new introduction, Section 2 simplified, corrections made to Section