REMINDER: ICTP-SISSA Quot seminar - Thursday 20 March, at 14:30 - VENUE: Room 101, Enrico Fermi Building

[ICTP Math Section]

*_ICTP-SISSA Quot seminar_
*

VENUE: room 101, Enrico Fermi Building, Thursday 20 March @ 14:30


Organizers: B. Fantechi (SISSA), L. Gottsche (ICTP), A. Marian (ICTP), 
A. Ricolfi (SISSA), S. Sinha (ICTP)

Speaker: Ajay Gautam (ICTP/SISSA)


Title: Cohomology of the Quot scheme of rank zero quotients on smooth 
projective curves


Abstract: The geometry and topology of the Quot schemes of rank zero 
quotients on smooth projective curves has been studied quite extensively 
in the works of Strømme (1981), Bifet (1989), Chen (2001), 
Bifet-Ghione-Letizia (1994), Marian-Oprea (2007), Marian-Negut (2023) 
and several others. The Quot scheme in this case is a smooth projective 
variety. The work of Marian-Negut describes the additive structure on 
the cohomology, which provides a natural way of computing Poincaré 
polynomials (these had been known before by the work of Bifet and Chen). 
In this seminar I would like to explain the multiplicative structure on 
the cohomology. One can give a satisfactory account of this for the Quot 
scheme over P^1. Such a description for a general curve is a work in 
progress; I will highlight some difficulties one encounters in this 
case. Finally, if time permits, I would like to talk about the 
connection of the Quot scheme on P^1 to the stack of bundles and use it 
to give a geometric description of certain relations appearing in the 
presentation of its cohomology ring.
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https://indico.ictp.it/event/10993//

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