Compact moduli spaces of stable bundles on Kodaira surfaces

Abstract: In this talk, I will examine the geometry of moduli spaces of stable bundles on Kodaira surfaces, which are non-Kaehler compact surfaces that can be realised as torus fibrations over elliptic curves. These moduli spaces are interesting examples of holomorphic symplectic manifolds whose geometry is similar to the geometry of Mukai's moduli spaces on K3 and abelian surfaces. In particular, for certain choices of rank and Chern classes, the moduli spaces are themselves Kodaira surfaces. This is joint work with Marian Aprodu and Matei Toma.