Sequences of stable bundles over compact complex surfaces

Groups of Complex Line Bundles Over Compact Kähler Varieties.

Stable bundles on hypercomplex surfaces

A hypercomplex manifold is a manifold equipped with three complex structures I, J,K satisfying the quaternionic relations. Let M be a 4-dimensional compact smooth manifold equipped with a hypercomplex structure, and E be a vector bundle on M . We show that the moduli space of anti-self-dual connections on E is also hypercomplex, and admits a strong HKT metric. We also study manifolds with (4,4)...

Atoroidal surface bundles over surfaces

The main aim of this paper is to prove a finiteness result for atoroidal surface bundles over surfaces. It can be viewed from a number of different perspectives, and one can give several essentially equivalent statements. This, and related questions, have been considered by a number of authors. See [R] for a recent survey. First, we express it in group theoretical terms. By a surface group we m...

Stable vector bundles on algebraic surfaces

We prove an existence result for stable vector bundles with arbitrary rank on an algebraic surface, and determine the birational structure of certain moduli space of stable bundles on a rational ruled surface.

Sections of Fiber Bundles over Surfaces

We study the existence problem and the enumeration problem for sections of Serre fibrations over compact orientable surfaces. When the fundamental group of the fiber is finite, a complete solution is given in terms of 2-dimensional cohomology classes associated with certain irreducible representations of this group. The proofs are based on Topological Quantum Field Theory. AMS Subject classific...