PreprintarXiv licencearXiv
GKZ Systems and Gauss-Manin Connections of Families of Projective Hypersurfaces
Abstract
Periods of projective hypersurfaces satisfy GKZ hypergeometric systems, which may have solutions that do not arise as periods. For deformations of Fermat hypersurfaces, we describe the Gauss-Manin connection in terms of images of contiguity operators between GKZ systems. These images are also realized as Fourier transforms of minimal extensions of Kummer modules.
Related
- Gauss--Manin connections extend to holonomic coadmissible D-cap-modules
- Projective connections on super Heisenberg coinvariants. I
- Algebraic hyperbolicity of very general hypersurfaces in projective spaces
- Retraction of the complement of smooth projective hypersurfaces to an n-dimensional Δ-complex
- Stability conditions and moduli spaces on projective families
BibTeX
@misc{negishi2026systems,
title = {{GKZ Systems and Gauss-Manin Connections of Families of Projective Hypersurfaces}},
author = {Ryo Negishi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33602},
eprint = {2610.33602},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33602},
}
RIS
TY - UNPB
TI - GKZ Systems and Gauss-Manin Connections of Families of Projective Hypersurfaces
AU - Ryo Negishi
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33602
UR - https://arxiv.org/abs/2610.33602
AB - Periods of projective hypersurfaces satisfy GKZ hypergeometric systems, which may have solutions that do not arise as periods. For deformations of Fermat hypersurfaces, we describe the Gauss-Manin connection in terms of images of contiguity operators between GKZ systems. These images are also realized as Fourier transforms of minimal extensions of Kummer modules.
ER -