Moduli spaces of spacefilling branes in symplectic 4-manifolds

Abstract

On a symplectic manifold $(M,\omega )$, a spacefilling brane structure is a closed 2-form $F$ which determines a complex structure, with respect to which $F+i\omega$ is holomorphic symplectic. For holomorphic symplectic compact Kähler 4-manifolds, we show that the moduli space of spacefilling branes is smooth, and determine its dimension. The proof relies on the local Torelli theorem for K3 surfaces and tori.

24 pages. Exposition slightly improved. Final version accepted for publication