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.