Hypergeometric functions and mirror symmetry in toric varieties

1999/12/14 by R. Paul Horja, Richard Paul Horja, Horja, Richard Paul · 5 citations
Computer Science · Mathematics · Physics and Astronomy · #14J32 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation #math.AG #msc:14J32

paper · pdf · doi:10.48550/arxiv.math/9912109

LaTeX, 103 pages, 4 figures. Clarifications added in the introduction

openalex publication_date 1999/12/14 · arxiv created 2000/02/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties

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• Moduli, Motives, Mirrors (Plenary talk at the 3rd ECM, Barcelona, July 10-14, 2000)
• Artin group actions on derived categories of threefolds
• Two-Sphere Partition Functions and Gromov-Witten Invariants

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