Hypergeometric systems from groups with torsion
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912760420368384 |
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| author | Reichelt, Thomas Sevenheck, Christian Walther, Uli |
| author_facet | Reichelt, Thomas Sevenheck, Christian Walther, Uli |
| contents | We consider $A$-hypergeometric (or GKZ-)systems in the case where the grading (character) group is an arbitrary finitely generated Abelian group. Emulating the approach taken for classical GKZ-systems in arXiv:math/0406383 that allows for a coefficient module, we show that these $D$-modules are holonomic systems. For this purpose we formulate an Euler--Koszul complex in this context, built on an extension of the category of $A$-toric modules. We derive that these new systems are regular holonomic under circumstances that are similar to those that lead to regular holonomic classical GKZ-systems.
For the appropriate coefficient module, our $D$-modules specialize to the "better behaved GKZ-systems" introduced by Borisov and Horja. We certify the corresponding $D$-modules as regular holonomic, and establish a holonomic duality on the level of $D$-modules that was suggested on the level of solutions by Borisov and Horja and later shown by Borisov and Han in a special situation (arXiv:1308.2238, arXiv:2301.01374). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00762 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hypergeometric systems from groups with torsion Reichelt, Thomas Sevenheck, Christian Walther, Uli Algebraic Geometry 32C38, 14F10, 32S40 We consider $A$-hypergeometric (or GKZ-)systems in the case where the grading (character) group is an arbitrary finitely generated Abelian group. Emulating the approach taken for classical GKZ-systems in arXiv:math/0406383 that allows for a coefficient module, we show that these $D$-modules are holonomic systems. For this purpose we formulate an Euler--Koszul complex in this context, built on an extension of the category of $A$-toric modules. We derive that these new systems are regular holonomic under circumstances that are similar to those that lead to regular holonomic classical GKZ-systems. For the appropriate coefficient module, our $D$-modules specialize to the "better behaved GKZ-systems" introduced by Borisov and Horja. We certify the corresponding $D$-modules as regular holonomic, and establish a holonomic duality on the level of $D$-modules that was suggested on the level of solutions by Borisov and Horja and later shown by Borisov and Han in a special situation (arXiv:1308.2238, arXiv:2301.01374). |
| title | Hypergeometric systems from groups with torsion |
| topic | Algebraic Geometry 32C38, 14F10, 32S40 |
| url | https://arxiv.org/abs/2402.00762 |