Variability sets on Riemann surfaces and forgetful maps between Teichmüller spaces.
We show that certain moduli spaces of vector bundles over blown-up primary Hopf surfaces admit no compact components. These are the moduli spaces used by Andrei Teleman in his work on the classification of class VII surfaces.
We study holomorphic vector bundles on non-algebraic compact manifolds, especially on tori. We exhibit phenomena which cannot occur in the algebraic case, e.g. the existence of 2-bundles that cannot be obtained as extensions of a sheaf of ideals by a line bundle. We prove some general theorems in deformations theory of bundles, which is our main tool.
We classify Veech groups of tame non-compact flat surfaces. In particular we prove that all countable subgroups of ) avoiding the set of mappings of norm less than 1 appear as Veech groups of tame non-compact flat surfaces which are Loch Ness monsters. Conversely, a Veech group of any tame flat surface is either countable, or one of three specific types.