Combinatorics of rank jumps in simplicial hypergeometric systems

DOI10.1090/S0002-9939-05-08245-6zbMath1090.33005arXivmath/0402071MaRDI QIDQ3372122

Laura Felicia Matusevich, Ezra Miller

Publication date: 17 February 2006

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0402071

zbMATH Keywords

local cohomology modulesimplicial\(A\)-hypergeometric systems\(A\)-hypergeometric modulecombinatorics of \(\mathbb Z^d\)-graded local cohomologylocal cohomology for semigroup ringsrank-jumping parameter

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Ordinary and skew polynomial rings and semigroup rings (16S36) Other hypergeometric functions and integrals in several variables (33C70) Local cohomology and commutative rings (13D45) Commutative rings of differential operators and their modules (13N10) Semigroup rings, multiplicative semigroups of rings (20M25) Cohen-Macaulay modules (13C14)

Related Items

Homological methods for hypergeometric families ⋮ Graded local cohomology of modules over semigroup rings ⋮ Exponential growth of rank jumps for \(A\)-hypergeometric systems ⋮ $D$-module structure of local cohomology modules of toric algebras

Uses Software

• CoCoA
• Macaulay2
• SINGULAR

Cites Work

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• Hypergeometric functions and rings generated by monomials
• Logarithm-free \(A\)-hypergeometric series
• The \({\mathcal A}\)-hypergeometric system associated with a monomial curve
• Algorithms for graded injective resolutions and local cohomology over semigroup rings
• Hypergeometric functions and toric varieties
• Homological methods for hypergeometric families