Invariants of hypergeometric groups for Calabi-Yau complete intersections in weighted projective spaces

TL;DR

This paper investigates the invariants of hypergeometric groups linked to Calabi-Yau complete intersections in weighted projective spaces, revealing a one-dimensional space of quadratic invariants related to derived category structures.

Contribution

It establishes that the quadratic invariants form a one-dimensional space spanned by the Gram matrix of a derived category generator, connecting hypergeometric group invariants to algebraic geometry.

Findings

The space of quadratic invariants is one-dimensional.

The invariants are spanned by the Gram matrix of a derived category generator.

Links between hypergeometric group invariants and derived categories are established.

Abstract

Let Y be a Calabi-Yau complete intersection in a weighted projective space. We show that the space of quadratic invariants of the hypergeometric group associated with the twisted I-function is one-dimensional, and spanned by the Gram matrix of a split-generator of the derived category of coherent sheaves on Y with respect to the Euler form.