Algebraic and Arithmetic Geometry Seminar

Vafa-Witten formulas and generalizations

by Lothar Göttsche (ICTP, Trieste)

Aula Magna (Dipartimento di Matematica)

Aula Magna

Dipartimento di Matematica


25 years ago Vafa and Witten predicted generating functions for the Euler numbers of the moduli spaces of sheaves on algebraic surfaces. In this talk, I review joint work with Martijn Kool to interpret and check these predictions in terms of virtual Euler numbers, and to extend them to finer invariants like $chi_y$ genus. Time permitting I will also mention recent results on Chern numbers of tautological sheaves, and Verlinde type formulas.