FRG workshop, 2011

J. Sawon

Title: Deformations of generalized complex K3 surfaces


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.

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, as will be explained in this talk.