Seminar Algebra - Dr. D.C. Veniani

Title: The number of Enriques surfaces covered by a K3 surface

Abstract:
Given the transcendental lattice of a complex K3 surface X, I will show how to compute the number of non-isomorphic Enriques surfaces covered by X. In particular, I will describe the two 'most algebraic' Enriques surfaces covered by the singular K3 surface of discriminant 7 (j.w. Ichiro Shimada). Finally, I will explain how the search for K3 surfaces with no Enriques quotients turns into a question about integral quadratic forms representing 1, and how to answer it (j.w. Simon Brandhorst).