ICTP-SISSA - Algebraic Geometry Seminar - Friday, 20 January, at 16:00 hrs.

[Math Group]

M A T H E M A T I C S   S E M I N A R S   2017


Friday, 20 January, at 16:00 hrs.


Artan Sheshmani (Aarhus University and Harvard University)


Title: Nested Hilbert schemes and DT theory of local threefolds


Abstract: Following talk 1 we study the geometry of S which is 
projective simply connected complex surface and we let L be a line 
bundle on S. We study moduli space of stable compactly supported 
2-dimensional sheaves on the total spaces of L. The moduli space admits 
a C^*-action induced by scaling the fibers of L. We identify certain 
components of the fixed locus of the moduli space with the moduli space 
of torsion free sheaves on S and the nested Hilbert schemes on S. We 
define reduced Donaldson-Thomas invariants by virtual localization. When 
L is the canonical bundle of S these reduced DT invariants recover 
Vafa-Witten invariants defined by Tanaka-Thomas via the moduli space of 
Higgs pairs on S. Vafa-Witten invariants are expected to have modular 
properties predicted by S-duality. We further show that in this case, in 
combination with Mochizuki's formulas, we are able to express these 
equivariant Donaldson-Thomas invariants on the total space of canonical 
bundle of S in terms of our invariants of nested Hilbert schemes in talk 
1, the Seiberg-Witten invariants of S, and the integrals over the 
products of Hilbert schemes of points on S.


VENUE:  Luigi Stasi Seminar Room (ICTP Leonardo da Vinci Building, first 
floor)

-- 
Koutou Mabilo
ICTP Mathematics Group
Leonardo Da Vinci Building, room 106
Strada Costiera no. 11
34151 Trieste, Italy

Tel. no.: +39-040-2240455
math at ictp.it
http://math.ictp.it