ICTP/IGAP seminar on Algebraic Geometry - Wednesday, 2 February, at 16:00/hybrid

[ICTP/math - Mabilo Koutou]

ICTP/IGAP seminar on Algebraic Geometry:

Title: Moduli spaces of sheaves, Vafa-Witten formula and virtual
invariants

Speaker: Lothar Goettsche (ICTP)

Starts 2 Feb 2022 16:00
Ends 2 Feb 2022 17:00
Central European Time
Online/Presence

Venue: ICTP Leonardo Building - Luigi Stasi Seminar Room

Please Register in advance for this meeting:
https://zoom.us/meeting/register/tJUtceChpjoqGtSIFcTsOUO2mjL_M8RxHil9
After registering, you will receive a confirmation email containing
information about joining the meeting.

Abstract:
After the overview lecture of December, we start going through the
material in more detail:
We introduce the Hilbert scheme of points on a surface, define moduli
spaces of stable sheaves, and state the Vafa-Witten formula for the Euler
numberts of moduli spaces of rank 2 sheaves. Â  The moduli spaces of
sheaves are in general singular, of a dimension different from the
expected dimension. We introduce perfect obstruction theories and the
virtual fundamental class. Integrating cohomology classes against this
virtual fundamental class allows to define virtual versions of enumerative
invariants, which behave similar to the invariants of smooth varieties,
among them a virtual version of the Euler number.
We conjecture that the Vafa-Witten formula computes this virtual Euler
number.

This will be a hybrid seminar. All are very welcome to join either online
or in person (if provided with a green pass). Venue: Luigi Stasi seminar
room, for those wishing to attend in person.

More information are available at this page:
https://indico.ictp.it/event/9861/