##### Department of Mathematics,

University of California San Diego

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### Algebraic Geometry Seminar

## Sebastian Casaina-Martin

#### University of Colorado at Boulder

## Birational geometry of the moduli space of genus four curves

##### Abstract:

In addition to the Deligne-Mumford compactification for the moduli space of genus four curves, there are a number of additional compactifications that arise naturally. In this talk I will discuss joint work with Radu Laza where we compare some of these spaces. The description we obtain is similar to that for genus three curves (work of Hyeon-Lee), as well as to some previous results we have for the moduli space of cubic threefolds.

Host: Dragos Oprea

### October 22, 2009

### 4:00 PM

### AP&M 7218

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