Projective models of Enriques surfaces via elliptic curves

Abstract: Enriques surfaces form one of the four classes of algebraic surfaces of Kodaira dimension zero in the Enriques-Kodaira classification. The first examples of Enriques surfaces were constructed by Enriques as minimal desingularizations of certain non-normal sextics in P^3, which are now called Enriques sextics. The goal of this talk will be to show that every Enriques surface over an algebraically closed field of characteristic different from 2 can be realized as the minimal desingularization of an Enriques sextic. I will introduce the main tool used in the proof, namely isotropic sequences, and I will show how the presence of many elliptic fibrations on the surface leads to "good" projective models. I will then discuss some geometric implications of the result and some relevant examples. This is joint work in progress with Gebhard Martin and Davide Veniani.

algebraic geometrynumber theory

Audience: researchers in the topic

Leiden Algebra, Geometry, and Number Theory Seminar