Abstract by Joshua Fullwood
An Overview of the Theory of K3 Surfaces with Elliptic Fibration
If k is an algebraically closed field, then a smooth projective surface is elliptic if it possesses a
morphism onto a smooth projective curve such that almost all fibres of this morphism are
smooth curves of genus 1. This structure is called an elliptic fibration and the surface is called an elliptic surface. The theory of elliptic
surfaces plays a role in the general theory of algebraic surfaces. Furthermore, certain of these
surfaces, which are called elliptic K3 surfaces, play a role in the study of mirror symmetry. Some
elliptic K3 surfaces come equipped with a non-symplectic automorphism, and the curves on the elliptic surface invariant under this automorphism generate an integral lattice, which in turn is used to define mirror symmetry for these particular surfaces.
In this talk, we'll review some of the theory of elliptic surfaces, and describe how to construct the invariant lattice of a given non-symplectic automorphism.