The singular locus of Lauricella's \(F_C\)

DOI10.2969/jmsj/06630981zbMath1312.33043arXiv1110.6675OpenAlexW2963260406MaRDI QIDQ743700

Nobuki Takayama, Ryohei Hattori

Publication date: 30 September 2014

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

Full work available at URL: https://arxiv.org/abs/1110.6675

zbMATH Keywords

Gröbner basissingular locus\(D\)-module\(A\)-hypergeometric systemsLauricella's hypergeometric differential equation

Mathematics Subject Classification ID

Sheaves of differential operators and their modules, (D)-modules (32C38) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10) Appell, Horn and Lauricella functions (33C65)

Related Items (9)

Factoring linear partial differential operators in \(n\) variables ⋮ Torus equivariant \(D\)-modules and hypergeometric systems ⋮ Feynman integrals in dimensional regularization and extensions of Calabi-Yau motives ⋮ Counting the number of master integrals for sunrise diagrams via the Mellin-Barnes representation ⋮ Restrictions of Pfaffian systems for Feynman integrals ⋮ Monodromy representations of hypergeometric systems with respect to fundamental series solutions ⋮ Picard–Vessiot groups of Lauricella's hypergeometric systems EC and Calabi–Yau varieties arising integral representations ⋮ Algebraic analysis of the hypergeometric function \(_1F_1\) of a matrix argument ⋮ Lauricella's \(F_C\) with finite irreducible monodromy group

Cites Work

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• Resonance equals reducibility for \(A\)-hypergeometric systems
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• Monodromy group of Appell's system (\(F_ 4)\)
• On the maximally overdetermined system of linear differential equations. I
• Computation of the characteristic variety and the singular locus of a system of differential equations with polynomial coefficients
• Gröbner deformations of hypergeometric differential equations
• Hypergeometric functions and toric varieties
• Algorithms for \(D\)-modules -- restriction, tensor product, localization, and local cohomology groups

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