Modul:   MAT770  Oberseminar: Algebraische Geometrie

Invariants of moduli of sheaves on general type surfaces

Vortrag von Prof. Dr. Martijn Kool

Sprecher eingeladen von: Prof. Dr. Christian Okonek

Datum: 27.11.17  Zeit: 13.15 - 14.45  Raum: Y27H25

Based on a formula from Vafa-Witten, we conjecture an expression for the virtual Euler characteristics of moduli spaces of rank 2 stable sheaves on general type surfaces. We provide several conjectural refinements e.g. to virtual cobordism class. We write these invariants in terms of Donaldson invariants, which---by Mochizuki's theory---can be expressed in terms of Seiberg-Witten invariants and integrals over Hilbert schemes of points. These integrals are determined by their values on P^2 and P^1 x P^1, which allows us to check our conjecture in many cases. Joint with Lothar Göttsche.