Stable vector bundles on algebraic surfaces

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.

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)...

Vector Bundles on Riemann Surfaces

1. Differentiable Manifolds 2 2. Complex Manifolds 3 2.1. Riemann Surfaces of Genus One 4 2.2. Constructing Riemann Surfaces as Curves in P 6 2.3. Constructing Riemann Surfaces as Covers 9 2.4. Constructing Riemann Surfaces by Glueing 10 3. Topological Vector Bundles 11 3.1. The Tangent and Cotangent Bundles 13 3.2. Interlude: Categories, Complexes and Exact Sequences 14 3.3. Metrics on Vector ...

Stable Real Algebraic Vector Bundles over a Klein Bottle

Let X be a geometrically connected smooth projective curve of genus one, defined over the field of real numbers, such that X does not have any real points. We classify the isomorphism classes of all stable real algebraic vector bundles over X .

Vector bundles over algebraic curves