Twisted Homogeneous Coordinate Rings of Abelian Surfaces via Mirror Symmetry

Abstract

In this paper we study Seidel's mirror map for abelian and Kummer surfaces. We find that mirror symmetry leads in a very natural way to the classical parametrization of Kummer surfaces in $\P^3$. Moreover, we describe a family of embeddings of a given abelian surface into noncommutative projective spaces.