Wall-crossing for punctual Quot-schemes

16.11.2021 13:15 - 14:45

Arkadij Bojko (ETH Zurich)

Hilbert schemes of points for a surface are a well studied subject with many famous results like Göttsche's formula for its Betti numbers. A natural generalization comes from studying Grothendieck's Quot-schemes and the associated enumerative invariants. Unlike the former, punctual Quot-schemes are smooth only virtually admitting perfect obstruction theories and virtual fundamental classes. This has recently been used to study invariants counting zero-dimensional quotients of trivial vector bundles by multiple authors who used virtual localization and therefore could not treat the case of a general vector bundle. We rely on other techniques which use a general wall-crossing framework of D. Joyce to study these. These methods use lie algebra coming from vertex algebras constructed out of topological data. I will explain how these arise naturally in the Quot-scheme setting and how one can obtain explicit invariants and study their symmetries. 

Organiser:

H. Grobner, A. Minguez-Espallargas, A. Mellit

Location:

HS 10, 2. OG, OMP 1