Combinatorial aspects of mirror symmetry
Abstract
The purpose of this paper is to review some combinatorial ideas behind the mirror symmetry for Calabi-Yau hypersurfaces and complete intersections in Gorenstein toric Fano varieties. We suggest as a basic combinatorial object the notion of a Gorenstein polytope of index r. A natural combinatorial duality for d-dimensional Gorenstein polytopes of index r extends the well-known polar duality for reflexive polytopes (case r=1). We consider the Borisov duality between two nef-partitions as a duality between two Gorenstein polytopes P and P^* of index r together with selected special (r-1)-dimensional simplices S in P and S' in P^*. Different choices of these simplices suggest an interesting relation to Homological Mirror Symmetry.
Cite
@article{arxiv.math/0703456,
title = {Combinatorial aspects of mirror symmetry},
author = {Victor Batyrev and Benjamin Nill},
journal= {arXiv preprint arXiv:math/0703456},
year = {2008}
}
Comments
AMS-LaTeX, 37 pages, 3 figures; conjecture 4.10 refined, bibliography updated