##### Department of Mathematics,

University of California San Diego

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### Math 292 - Topology Seminar

## Justin Sawon

#### UNC

## Deformations of generalized complex K3 surfaces

##### Abstract:

\indent A generalized complex structure (as introduced by Hitchin) consists of a complex structure on the direct sum of the tangent and cotangent bundles of a manifold, satisfying a certain integrability condition. A complex manifold can be regarded as a generalized complex manifold in a canonical way. This leads to an enlarged space of deformations: in addition to deformations as a complex manifold, there are also non-commutative and gerby deformations. \indent Symplectic manifolds can also be regarded as generalized complex manifolds. For K3 surfaces, a complex structure can be deformed via generalized complex structures to a symplectic structure. It appears that these deformations connect pairs of Fourier-Mukai equivalent K3s to pairs of mirror K3s. \indent This talk will be an introduction to generalized complex geometry, leading to a description of the above phenomena.

### May 10, 2011

### 10:30 AM

### AP&M 7218

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