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Mini-school on moduli of sheaves on three- and four-folds

December 15, 2020 @ 9:00 am - 11:30 am

Mini-school on moduli of sheaves on three- and four-folds

Hosted by: Justin Sawon

Email sawon@email.unc.edu for more information.

“Mini-school” on some topics in algebraic geometry. The speakers are Laura Pertusi (Universita degli Studi di Milano) and our new postdoc Xuqiang Qin:

http://www.mat.unimi.it/users/pertusi/

https://qinxuqiang.github.io/

The schedule is (all times are Eastern Standard Time):

Monday 14th December
9-10am             Qin talk 1

10:30-11:30am Pertusi talk 1

Tuesday 15th December

9-10am             Qin talk 2
10:30-11:30am Pertusi talk 2
Speaker: Xuqiang Qin
Talk 1: Introduction to derived categories and semiorthogonal decompositions

Abstract: I will give a quick introduction to the derived categories of coherent sheaves on a smooth projective variety and its structure as a triangulated category. I will talk about the notion of a semiorthogonal decomposition and provide examples of it on Fano varieties.

Talk 2: Compactification of moduli space of instantons on the Fano 3-folds

Abstract: Instanton bundles are a class of stable vector bundles with nice cohomology vanishing properties.  In this talk I will describe natural compactifications of moduli spaces of instantons on some Fano 3-folds of Picard rank 1 and index 2.

Speaker: Laura Pertusi

Talks 1+2: Bridgeland stability conditions and Kuznetsov components of Fano threefolds and fourfolds

Abstract: As first observed by Kuznetsov, the bounded derived category of a Fano variety admits a semiorthogonal decomposition whose non-trivial component encodes much informations about the geometry of the variety. On the other hand, stability conditions as introduced by Bridgeland provide a powerful tool to study triangulated categories and moduli spaces of objects in them. The aim of these two talks is to survey some recent results about the construction of stability conditions on the Kuznetsov component of Fano threefolds (of Picard rank 1 and index 2), on cubic fourfolds and Gushel–Mukai fourfolds, and the related moduli spaces.

In the first talk we will recall the definition of (weak) stability conditions on a triangulated category, the construction via tilt stability on surfaces and threefolds à la Bayer-Macrì-Toda and the method to induce stability conditions on Kuznetsov components proved by Bayer-Lahoz-Macrì-Stellari. In the second talk, we will discuss some results about moduli spaces in the case of cubic threefolds, cubic fourfolds and Gushel–Mukai fourfolds obtained in joint works with Yang, and Li-Zhao, and Perry-Zhao, respectively.

Details

Date:
December 15, 2020
Time:
9:00 am - 11:30 am
Event Category: