Examples of hypergeometric twistor
𝒟-modules

Domínguez, Alberto Castaño; Reichelt, Thomas; Sevenheck, Christian

doi:10.2140/ant.2019.13.1415

Cited by 5 publications

(3 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Another application of our main result, which can be found in the two recent papers [CS19] and [CRS19], is the calculation of the so-called irregular Hodge filtration on certain 1-dimensional classical hypergeometric modules. The irregular Hodge filtration has been introduced by Sabbah [Sab18] in order to attach Hodge-type numerical invariants (namely dimensions of graded parts of a filtration) to differential systems acquiring irregular singularities.…”

Section: Introductionmentioning

confidence: 91%

“…It turns out that confluent classical hypergeometric modules (these are precisely those with irregular singularities) are obtained from GKZ systems by a dimensional reduction and a Fourier-Laplace transformation. Using our result (that is, Theorem 5.35), one can explicitly describe the irregular Hodge filtration (and give closed formulas for irregular Hodge numbers) of certain such systems (see [CS19,Theorem 4.7] and [CRS19,Theorem 5.9] for more details).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Hypergeometric Hodge modules

Sevenheck¹

2020

Alg. Geom.

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Hypergeometric Hodge modules

Sevenheck¹

2020

Alg. Geom.

Self Cite

View full text Add to dashboard Cite

show abstract

“…In [6] and [21], they introduced and studied exponential R-module "E f " as a twistor D-module. Moreover, in Domíngez-Reichelt-Sevenheck [3] and Mochizuki [9], they defined (with a slightly different formulation in each paper) the Fourier-Laplace transform of an integrable R-module or an integrable mixed twistor D-module on C n . The content of this subsection is a review and restatement of these papers, so there are essentially no original contents.…”

Section: Annales De L'institut Fouriermentioning

confidence: 99%

The Hodge filtration of a monodromic mixed Hodge module and the irregular Hodge filtration

Saito

2024

Annales De l'Institut Fourier

View full text Add to dashboard Cite

For an algebraic vector bundle E over a smooth algebraic variety X, a monodromic D-module on E is decomposed into a direct sum of some Omodules on X. We show that the Hodge filtration of a monodromic mixed Hodge module is decomposed with respect to the decomposition of the underlying Dmodule. By using this result, we endow the Fourier-Laplace transform M ∧ of the underlying D-module M of a monodromic mixed Hodge module with a mixed Hodge module structure. Moreover, we describe the irregular Hodge filtration on M ∧ concretely and show that it coincides with the Hodge filtration at all integer indices.Résumé. -Pour un fibré vectoriel algébrique E sur une variété algébrique lisse X, un D-module monodromique sur E est décomposé en une somme directe de certains O-modules sur X. Nous montrons que la filtration de Hodge d'un module de Hodge mixte monodromique est décomposée par rapport à la décomposition du D-module sous-jacent. En utilisant ce résultat, nous munissons la transformée de Fourier-Laplace M ∧ du D-module sous-jacent M à un module de Hodge mixte monodromique d'une structure de module de Hodge mixte. De plus, nous décrivons explicitement la filtration de Hodge irrégulière sur M ∧ et montrons qu'elle coïncide avec la filtration de Hodge aux indices entiers.

show abstract

Algebraic aspects of hypergeometric differential equations

et al. 2021

View full text Add to dashboard Cite

We review some classical and modern aspects of hypergeometric differential equations, including A-hypergeometric systems of Gel$$'$$ ′ fand, Graev, Kapranov and Zelevinsky. Some recent advances in this theory, such as Euler–Koszul homology, rank jump phenomena, irregularity questions and Hodge theoretic aspects are discussed with more details. We also give some applications of the theory of hypergeometric systems to toric mirror symmetry.

show abstract

Examples of hypergeometric twistor 𝒟-modules

Cited by 5 publications

References 13 publications

Hypergeometric Hodge modules

Hypergeometric Hodge modules

The Hodge filtration of a monodromic mixed Hodge module and the irregular Hodge filtration

Algebraic aspects of hypergeometric differential equations

Contact Info

Product

Resources

About