Abstract: Last time we used nested Hilbert schemes to express vertical Vafa-Witten invariants of a surface S in terms of (unknown) universal power series, which are generating functions for intersection numbers on Hilbert schemes of points on S. In this lecture we will reduce to the case that the surface S is toric, and then explain how to explicitly compute the generating functions via localization. We will present the formulas obtained. Next time we will sketch how to use Mochizuki's formula to do the same for the horizontal Vafa-Witten invariants.
This will be a hybrid seminar. All are very welcome to join either online or in person. Venue: Luigi Stasi seminar room, for those wishing to attend in person.