HMS symmetries and hypergeometric systems

TL;DR

This paper explores the connection between symmetries in derived categories of algebraic varieties, homological mirror symmetry, and hypergeometric systems, focusing on toric varieties and their associated differential equations.

Contribution

It provides an expositional analysis of how categorical symmetries relate to hypergeometric systems within the framework of homological mirror symmetry for toric varieties.

Findings

Identifies categorical symmetries arising from derived categories.

Connects these symmetries to hypergeometric differential equations.

Offers insights into the mirror symmetry conjectural framework.

Abstract

The derived category of an algebraic variety might be a source of a myriad of new (categorical) symmetries. Some are predicted by homological mirror symmetry, to be obtained from the fundamental group of the space of complex structures of its mirror partner. These finally lead to differential equations. We expositorily unravel a part of this conjectural master plan for a class of toric varieties.