English

Geometric realisation of hypergeometric local systems

Algebraic Geometry 2026-02-17 v1

Abstract

We prove a realisation theorem for irreducible hypergeometric local systems defined over the rational numbers in terms of families of affine varieties in algebraic tori. The families we consider have been studied extensively in the literature and appear in mirror symmetry. Our result holds unconditionally for families with one-dimensional or even-dimensional fibres. It holds under a monodromy assumption for families with fibres of odd dimension greater than one.

Keywords

Cite

@article{arxiv.2602.14204,
  title  = {Geometric realisation of hypergeometric local systems},
  author = {Asem Abdelraouf and Giulia Gugiatti},
  journal= {arXiv preprint arXiv:2602.14204},
  year   = {2026}
}

Comments

37 pages, 3 figures, 1 table. Comments are welcome

R2 v1 2026-07-01T10:37:36.183Z