Enumerative Geometry of Orbifold K3 Surfaces

Abstract: Two of the most celebrated theorems in enumerative geometry (both predicted by string theorists) surround curve-counting for K3 surfaces. The Yau-Zaslow formula computes the honest number of rational curves in a K3 surface, and was generalized to the Katz-Klemm-Vafa formula computing the (virtual) number of curves of any genus. In this talk, I will review this story and then describe a recent generalization to orbifold K3 surfaces. One interpretation of the new theory is as producing a virtual count of curves in the orbifold, where we track both the genus of the curve and the genus of the corresponding invariant curve upstairs. As one example, we generalize the counts of hyperelliptic curves in an Abelian surface carried out by Bryan-Oberdieck-Pandharipande-Yin. This is work in progress with Jim Bryan.

algebraic geometrynumber theory

Audience: researchers in the topic

SFU NT-AG seminar

Series comments: Description: Research/departmental seminar

Seminar usually meets in-person. For online editions, the Zoom link is shared via mailing list.