Speaker: Roberto Laface

Title: Decomposition of singular Abelian Surfaces

Abstract: Decomposition of singular Abelian Surfaces Abstract: Inspired by a work of Ma, in which he counts the number of decompositions of abelian surfaces by lattice-theoretical tools, we explicitly find all such decompositions in the case of singular abelian surfaces. This is done by computing the transcendental lattice of products of isogenous elliptic curves with complex multiplication, generalizing a technique of Shioda and Mitani, and by studying the action of a certain class group act on the factors of a given decomposition. Incidentally, our construction provides us with an alternative and simpler formula for the number of decompositions, which is obtained via an enumeration argument. Also, we give an application of this result to singular K3 surfaces.