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: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

We normally meet in-person in the indicated room. For online editions, we use Zoom and distribute the link through the mailing list. If you wish to be put on the mailing list, please subscribe to ntag-external using lists.sfu.ca