On the rank of an A$A$‐hypergeometric D$D$‐module versus the normalized volume of A$A$

DOI10.1112/blms.12567zbMath1520.13041arXiv1907.08669MaRDI QIDQ6175398

Christine Berkesch Zamaere, María Cruz Fernández-Fernández

Publication date: 18 August 2023

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.08669

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Other hypergeometric functions and integrals in several variables (33C70) Sheaves of differential operators and their modules, (D)-modules (32C38) Commutative rings of differential operators and their modules (13N10)

Cites Work

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• Resonance equals reducibility for \(A\)-hypergeometric systems
• Duality and monodromy reducibility of \(A\)-hypergeometric systems
• Hypergeometric functions and rings generated by monomials
• Gröbner deformations of hypergeometric differential equations
• The \({\mathcal A}\)-hypergeometric system associated with a monomial curve
• Exponential growth of rank jumps for \(A\)-hypergeometric systems
• Hypergeometric functions and toric varieties
• The rank of a hypergeometric system
• A-Hypergeometric ranks for toric threefolds
• On the parametric behavior of $A$-hypergeometric series
• Arbitrary rank jumps forA-hypergeometric systems through Laurent polynomials
• Homological methods for hypergeometric families
• Rings of Invariants of Tori, Cohen-Macaulay Rings Generated by Monomials, and Polytopes

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