Algebraic aspects of hypergeometric differential equations

DOI10.1007/s13366-020-00560-1zbMath1468.14042arXiv2004.07262OpenAlexW3128641715WikidataQ115375911 ScholiaQ115375911MaRDI QIDQ2022362

Thomas Reichelt, Uli Walther, Christian Sevenheck, Mathias Schulze

Publication date: 29 April 2021

Published in: Beiträge zur Algebra und Geometrie (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.07262

zbMATH Keywords

hypergeometric functionsHodge filtrationweight filtrationLandau-Ginzburg modelshypergeometric systemsGKZ systemsEuler-Koszul complexirregular Hodge filtrationirregularity of D-modules

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) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10) Commutative rings of differential operators and their modules (13N10) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) Mirror symmetry (algebro-geometric aspects) (14J33)

Related Items

Weight filtrations on GKZ-systems, Local Cohomology—An Invitation, Nonlinear algebra and applications, Algebraic analysis of the hypergeometric function \(_1F_1\) of a matrix argument, On Feynman graphs, matroids, and GKZ-systems, Hypergeometric Functions and Feynman Diagrams

Cites Work

• Irregular Hodge numbers of confluent hypergeometric differential equations
• Gevrey Expansions of Hypergeometric Integrals I
• Logarithmic Frobenius manifolds, hypergeometric systems and quantum 𝒟-modules
• Confluent A-hypergeometric functions and rapid decay homology cycles
• Irregular modified $A$-hypergeometric systems
• ON THE IRREGULAR HODGE FILTRATION OF EXPONENTIALLY TWISTED MIXED HODGE MODULES
• Quantum 𝒟-modules for toric nef complete intersections
• Equivariant Gromov - Witten Invariants
• Arbitrary rank jumps forA-hypergeometric systems through Laurent polynomials
• Homological methods for hypergeometric families
• Non-affine Landau-Ginzburg models and intersection cohomology
• Nilpotent orbits of a generalization of Hodge structures
• Rings of Invariants of Tori, Cohen-Macaulay Rings Generated by Monomials, and Polytopes
• IRREGULAR HODGE FILTRATION OF SOME CONFLUENT HYPERGEOMETRIC SYSTEMS
• Mixed Hodge modules
• Irreducible components of characteristic varieties.
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hypergeometric functions for projective toric curves
• Monodromy of \(A\)-hypergeometric functions
• On the better behaved version of the GKZ hypergeometric system
• Resonance equals reducibility for \(A\)-hypergeometric systems
• Monodromies at infinity of confluent \(A\)-hypergeometric functions
• Towards mirror symmetry for varieties of general type
• Modules de Hodge polarisables. (Polarisable Hodge modules)
• Gevrey solutions of irregular hypergeometric systems in two variables
• Monodromy at infinity of \(A\)-hypergeometric functions and toric compactifications
• Irreducibility of \(A\)-hypergeometric systems
• Pfaffian systems of \(A\)-hypergeometric equations. I: Bases of twisted cohomology groups.
• Hypergeometric series representations of Feynman integrals by GKZ hypergeometric systems
• Periods for flat algebraic connections
• An integral structure in quantum cohomology and mirror symmetry for toric orbifolds
• Limits of families of Brieskorn lattices and compactified classifying spaces
• A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory.
• Local cohomology modules of \(A\)-hypergeometric system of Cohen-Macaulay type
• Mellin--Barnes integrals as Fourier--Mukai transforms
• \(D\)-modules, perverse sheaves, and representation theory. Translated from the Japanese by Kiyoshi Takeuchi
• Hypergeometric periods for a tame polynomial
• Quantum Riemann-Roch, Lefschetz and Serre
• Duality and monodromy reducibility of \(A\)-hypergeometric systems
• Irregularity of hypergeometric systems via slopes along coordinate subspaces
• Binomial \(D\)-modules
• Algebraic \(A\)-hypergeometric functions
• Irregular hypergeometric \(\mathcal D\)-modules
• Quantum \(D\)-modules and generalized mirror transformations
• Primitive collections and toric varieties
• The Riemann-Hilbert problem for holonomic systems
• On the structure of Brieskorn lattice
• Monodromy for the hypergeometric function \(_ nF_{n-1}\)
• Generalized Euler integrals and \(A\)-hypergeometric functions
• Variations of the mixed Hodge structure of affine hypersurfaces in algebraic tori
• Higher solutions of hypergeometric systems and Dwork cohomology
• Hypergeometric functions and rings generated by monomials
• The intrinsic normal cone
• Frobenius manifolds: Isomonodromic deformations and infinitesimal period mappings
• Radon and Fourier transforms for \(\mathcal D\)-modules.
• \(A\)-hypergeometric modules and Gauss-Manin systems
• Bounds on degrees of projective schemes
• On irregular binomial \(D\)-modules
• Solving algebraic equations in terms of \(\mathcal A\)-hypergeometric series
• Gröbner deformations of hypergeometric differential equations
• The \({\mathcal A}\)-hypergeometric system associated with a monomial curve
• On normalized Horn systems
• GKZ-hypergeometric systems for Feynman integrals
• Feynman integrals as A-hypergeometric functions
• On the local monodromy of \(A\)-hypergeometric functions and some monodromy invariant subspaces
• Dualizing, projecting, and restricting GKZ systems
• Examples of Hypergeometric twistor \(\mathcal{D}\)-modules
• Mixed twistor \(\mathcal D\)-modules
• The generalized confluent hypergeometric functions
• A mirror construction for the big equivariant quantum cohomology of toric manifolds
• Torus equivariant \(D\)-modules and hypergeometric systems
• Exponential growth of rank jumps for \(A\)-hypergeometric systems
• Euler-Mellin integrals and \(A\)-hypergeometric functions
• Singularities and holonomicity of binomial \(D\)-modules
• Systems of parameters and holonomicity of \(A\)-hypergeometric systems
• Monodromy of isolated singularities of hypersurfaces
• Hypergeometric D-modules and twisted Gauß-Manin systems
• Resonant Hypergeometric Systems and Mirror Symmetry
• Laurent polynomials, GKZ-hypergeometric systems and mixed Hodge modules
• Irreducible quotients ofA-hypergeometric systems
• The Structure of Bivariate Rational Hypergeometric Functions
• The rank of a hypergeometric system
• Gevrey solutions of the irregular hypergeometric system associated with an affine monomial curve
• Introduction to Toric Varieties. (AM-131)
• Harmonic Bundles on Noncompact Curves
• Fuchs and the theory of differential equations
• Hodge theoretic aspects of mirror symmetry
• Polygône de Newton et $b$-fonctions pour les modules microdifférentiels
• The Integrability of the Characteristic Variety
• Exponential Sums and Differential Equations. (AM-124)
• ALGEBRAIC APPELL-LAURICELLA FUNCTIONS
• Pentes algébriques et pentes analytiques d'un -module
• A mirror theorem for toric complete intersections
• APPELL'S F4 WITH FINITE IRREDUCIBLE MONODROMY GROUP
• Notes on stable maps and quantum cohomology
• APPELL'S HYPERGEOMETRIC SYSTEMS <i>F</i>₂ WITH FINITE IRREDUCIBLE MONODROMY GROUPS
• On the parametric behavior of $A$-hypergeometric series
• Variations of Hodge Structures for Hypergeometric Differential Operators and Parabolic Higgs Bundles
• Rigid irregular connections on ℙ¹
• Irregular Hodge theory
• Hypergeometric Hodge modules