Algebra / Topology Seminar

Speaker: Georg Oberdiek

Title: Enumerative geometry of K3 surfaces and modular forms

Abstract: K3 surfaces are complex algebraic surfaces which are two-dimensional analogues of elliptic curves. The study of their geometry goes back almost 200 years to work of Cayley, Kummer, Klein and many others. In this talk we consider the enumerative geometry of algebraic curves on K3 surfaces and their connection to modular forms. In the second part I will develop a parallel connection for the analogues of K3 surfaces in higher dimension, the hyper-Kähler varieties. For the punctual Hilbert schemes of a K3 surface (the prime example of Hyperkähler varieties) the counts of algebraic curves are related to Jacobi forms.