ICTP Mathematics Lecture 2 - 12 March 2019 at 14:30 (Lothar Göttsche)

[Math Section]

M A T H E M A T I C S   S E M I N A R S  2019

Tuesday 12 March 2019 at 14:30 hrs.

Lothar Göttsche (ICTP)


Title: Virtual topological invariants of moduli spaces of sheaves on 
surfaces II


Abstract:

     Using arguments from theoretical physics, Vafa and Witten gave a 
generating function for the Euler numbers of moduli spaces of rank 2 
coherent sheaves on algebraic surfaces.
     These moduli spaces are in general very singular, but they carry a 
perfect obstruction theory (they are virtually smooth). This gives 
virtual versions of many invariants of smooth projective varieties. Such 
virtual invariants occur everywhere in modern enumerative geometry, like 
Gromov-Witten invariants and Donaldson Thomas invariants, when 
attempting to make sense of the predictions from physics. We conjecture 
that the Vafa-Witten formula is true for the virtual Euler numbers. We 
confirm this conjecture in many examples. Then we give refinements of 
the conjecture.
      Our approach is based on Mochizuki's formula which reduces virtual 
intersection numbers on moduli spaces of sheaves to intersection numbers 
on Hilbert schemes of points.


VENUE:  IGAP (the old SISSA building) - As one can only enter the IGAP 
if one has a badge, people wanting to come should meet in the bar a few 
minutes earlier.


-- 
Monica Petronela Ancuta
for Ms Mabilo
Secretariat of the ICTP Mathematics Section
math at ictp.it

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