Basic Notions Seminar - Part I: Moduli spaces of sheaves on threefolds. Part II: Moduli spaces of rank 2 torsion-free sheaves with quasi-maximal third Chern class

[ICTP Math Section]

*Basic Notions Seminar *

*Date and Venue*: Monday 27 April at 14:30 - ICTP Leonardo Building 
Euler Lecture Hall

  * *Speaker: *Marcos Jardim (University of Campinas)

*Title Part I:* Moduli spaces of sheaves on threefolds

*Abstract:* While moduli spaces of sheaves on curves and surfaces are 
relatively well understood, understanding the case of varieties of 
dimension 3 is considered a hard problem. After giving a quick 
introduction to moduli spaces and sheaves, I will present the main 
problems and the challenges involved, as well as some of the results we 
have proved recently.
*
*

  * *Speaker: *Leonardo Silva de Oliveira (University of Campinas)

*Title Part II:* Moduli spaces of rank 2 torsion-free sheaves with 
quasi-maximal third Chern class
*
*
*Abstract:* Hartshorne established the irreducibility and smoothness of 
the Gieseker-Maruyama moduli spaces parameterizing semistable rank 2 
reflexive sheaves on P3 with c_1=-1 and the maximal third Chern class 
c_3 = c_2^2. Later, Okonek and Spindler and Schmidt, in an independent 
work, prove that this is still true for torsion-free sheaves. However, a 
gap theorem by Miró-Roig shows that the moduli space of reflexive 
sheaves is empty for a certain range on the c_3, including the 
quasi-maximal case c_3 = c_2^2 - 2. Despite the absence of reflexive 
sheaves, torsion-free sheaves do exist in this range, Almeida, Jardim, 
and Tikhomirov constructed a family of components for these spaces. In 
this talk we will use the modular Hartshorne-Serre correspondence to 
prove the irreducibility of M(-1, c_2, c_2^2 - 2) for c_2 =3.


All are welcome to join.

https://indico.ictp.it/event/11333/ <https://indico.ictp.it/event/11333/>

-- 
Micol Stock
Secretariat of the ICTP Math Section

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