Quot seminar - Thursday, April 3, at 14:30 - VENUE: SISSA in Room 137 - Solomiya Mizyuk

[ICTP Math Section]

*_Quot seminar_*

Thursday, April 3, at 14:30 - *_VENUE: SISSA in Room 137 _*_( Via 
Bonomea, 265, Trieste)_*_
_*



Speaker: Solomiya Mizyuk (SISSA)


Title: On the higher rank Donaldson-Thomas invariants of points


Abstract: Classical Donaldson-Thomas theory performs the virtual count 
of stable coherent sheaves with a given Chern character \gamma on a 
smooth projective threefold. In particular, if \gamma = (1, 0, 0, -n) 
the moduli space of interest is the Hilbert scheme of points, and the DT 
invariants are defined via a zero-dimensional perfect obstruction theory 
on it. We extend this story by considering the Quot scheme parametrizing 
zero-dimensional quotients of a locally free sheaf. We construct an 
almost perfect obstruction theory (a weaker version of a POT defined by 
Kiem and Savvas) on this Quot scheme which gives rise to a virtual class 
in degree zero and allows one to define higher rank invariants. We 
explain the computation of these new invariants in the toric case and, 
if time permits, discuss how to obtain the formula also in the general case.

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