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Twisted Homogeneous Coordinate Rings of Abelian Surfaces via Mirror Symmetry

Marco Aldi

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 $¶^3$. Moreover, we describe a family of embeddings of a given abelian surface into noncommutative projective spaces.

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 . Moreover, we describe a family of embeddings of a given abelian surface into noncommutative projective spaces.

Paper Structure

This paper contains 5 sections, 25 equations.

Table of Contents

  1. Introduction
  2. Seidel's mirror map for Kummer surfaces in $\mathbb P^3$
  3. Kummer surfaces in $\mathbb P^3$
  4. Seidel's Mirror Map
  5. Affine symplectomorphisms and algebras of Sklyanin type