Hypergeometric functions and mirror symmetry in toric varieties

TL;DR

This paper explores the relationship between automorphisms in categories related to homological mirror symmetry for Calabi-Yau complete intersections in toric varieties, providing explicit geometric constructions.

Contribution

It offers a new explicit geometric construction linking automorphisms of categories in the context of homological mirror symmetry for toric Calabi-Yau varieties.

Findings

Explicit geometric correspondence between automorphisms established

Supports Kontsevich's conjecture on automorphism groups

Advances understanding of mirror symmetry in toric geometry

Abstract

We study aspects related to Kontsevich's homological mirror symmetry conjecture in the case of Calabi-Yau complete intersections in toric varieties. In a 1996 lecture at Rutgers University, Kontsevich indicated how his proposal implies that the groups of automorphisms of the two types of categories involved in the homological mirror symmetry conjecture should also be identified. Our main results provide an explicit geometric construction of the correspondence between the automorphisms of the two types of categories.