##### Department of Mathematics,

University of California San Diego

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### Math 208: Seminar in Algebraic Geometry

## Prof. Samuel Grushevsky

#### Stony Brook

## Non-isomorphic compactifications of moduli of cubic surfaces

##### Abstract:

Moduli of cubic surfaces can be compactified from the point of view of geometric invariant theory (GIT), and from the point of view of the ball quotient. The Kirwan desingularization resolves the GIT singularities to yield a smooth Kirwan compactification, while the toroidal compactification of the ball quotient is also smooth. We show that these two smooth compactifications are, however, not isomorphic. Based on joint work with S. Casalaina-Martin, K. Hulek, R. Laza

Host: Elham Izadi

### February 24, 2023

### 3:30 PM

APM 7321

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