Perverse schobers and GKZ systems

Michel Van den Bergh; Špela Špenko

doi:10.1016/j.aim.2022.108307

Perverse schobers and GKZ systems

Michel Van den Bergh, Špela Špenko

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Perverse schobers are categorifications of perverse sheaves. In prior work we constructed a perverse schober on a partial compactification of the stringy Kähler moduli space (SKMS) associated by Halpern-Leistner and Sam to a quasi-symmetric representation of a reductive group. When the group is a torus the SKMS corresponds to the complement of the GKZ discriminant locus (which is a hyperplane arrangement in the quasi-symmetric case shown by Kite). We show here that a suitable variation of the perverse schober we constructed provides a categorification of the associated GKZ hypergeometric system in the case of non-resonant parameters. As an intermediate result we give a description of the monodromy of such "quasi-symmetric" GKZ hypergeometric systems

Original language	English
Article number	108307
Number of pages	60
Journal	Advances in Mathematics
Volume	402
DOIs	https://doi.org/10.1016/j.aim.2022.108307
Publication status	Published - 25 Jun 2022

Bibliographical note

Funding Information:
The second author is a senior researcher at the Research Foundation Flanders (FWO). While working on this project he was supported by the FWO grant G0D8616N: “Hochschild cohomology and deformation theory of triangulated categories”.

Publisher Copyright:
© 2022

Copyright:
Copyright 2022 Elsevier B.V., All rights reserved.

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abstract = "Perverse schobers are categorifications of perverse sheaves. In prior work we constructed a perverse schober on a partial compactification of the stringy K{\"a}hler moduli space (SKMS) associated by Halpern-Leistner and Sam to a quasi-symmetric representation of a reductive group. When the group is a torus the SKMS corresponds to the complement of the GKZ discriminant locus (which is a hyperplane arrangement in the quasi-symmetric case shown by Kite). We show here that a suitable variation of the perverse schober we constructed provides a categorification of the associated GKZ hypergeometric system in the case of non-resonant parameters. As an intermediate result we give a description of the monodromy of such {"}quasi-symmetric{"} GKZ hypergeometric systems",

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N2 - Perverse schobers are categorifications of perverse sheaves. In prior work we constructed a perverse schober on a partial compactification of the stringy Kähler moduli space (SKMS) associated by Halpern-Leistner and Sam to a quasi-symmetric representation of a reductive group. When the group is a torus the SKMS corresponds to the complement of the GKZ discriminant locus (which is a hyperplane arrangement in the quasi-symmetric case shown by Kite). We show here that a suitable variation of the perverse schober we constructed provides a categorification of the associated GKZ hypergeometric system in the case of non-resonant parameters. As an intermediate result we give a description of the monodromy of such "quasi-symmetric" GKZ hypergeometric systems

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Perverse schobers and GKZ systems

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