##### Department of Mathematics,

University of California San Diego

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### Algebraic Geometry Seminar

## Helge Ruddat

#### University of Mainz

## Skeleta of affine hypersurfaces

##### Abstract:

Any smooth affine hypersurface Z of complex dimension n deformation retracts to a cell complex of real dimension n. Starting from the Newton polytope of the defining equation of Z, I will give an explicit combinatorial construction of a compact space S, comprised of n-dimensional components, which embeds into Z as a deformation retract. In particular, Z is homotopy equivalent to S. The construction uses toric degenerations, Nakayama-Ogus's work in log geometry and the Kato-Nakayama space. It is motivated by the homological mirror symmetry program. If time permits, I will explain the connections. This work is joint with Nicola Sibilla, David Treumann and Eric Zaslow.

Host: Mark Gross

### April 26, 2013

### 4:00 PM

### AP&M 7321

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