##### Department of Mathematics,

University of California San Diego

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### Algebraic Geometry Seminar

## Andrei Jorza

#### Caltech

## Higher stable pair invariants for K3 surfaces

##### Abstract:

\indent Counting curves on threefolds has been defined in several conjecturally equivalent instances, by integrating with respect to a virtual class on a moduli space (of stable maps for Gromov-Witten theory, ideal sheaves for Donaldson-Thomas theory, and stable pairs for Pandharipande-Thomas theory). The analogous picture for K3 surfaces is incomplete. The Gromov-Witten theory has been calculated by Maulik, Pandharipande, and Thomas, and was shown to give rise to modular forms. In joint work with Benjamin Bakker we define and compute an analog of DT/PT theory on K3 surfaces via stable pairs and show that it similarly gives rise to modular forms on $\Gamma(4)$.

### November 30, 2011

### 3:00 PM

### AP&M 7218

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