##### Department of Mathematics,

University of California San Diego

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### Enumerative Geometry Seminar

## Svetlana Makarova

#### University of Pennsylvania

## Moduli spaces of stable sheaves over quasipolarized K3 surfaces, and Strange Duality

##### Abstract:

In this talk, I will talk about my construction of relative moduli spaces of stable sheaves over the stack of quasipolarized surfaces. For this, I first retrace some of the classical results in the theory of moduli spaces of sheaves on surfaces to make them work over the nonample locus. Then I will recall the theory of good moduli spaces, whose study was initiated by Alper and concerns an intrinsic (stacky) reformulation of the notion of good quotients from GIT. Finally, I use a criterion by Alper-Heinloth-Halpern-Leistner to prove existence of the good moduli space. The application of the construction that I have in mind is extending the Strange Duality results to degree two K3 surfaces - this part is still work in progress.

Host: Dragos Oprea

### December 2, 2020

### 12:00 PM

### Zoom Meeting ID: 947 1258 3008

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