Algebraic vector bundles on spheres

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.

Vector bundles over algebraic curves

Stably Trivial Equivariant Algebraic Vector Bundles

Let G be a reductive algebraic group over e, let F be a G-module, and let B be an affine G-variety, i.e., an affine variety with an algebraic action of G. Then B x F is in a natural way a G-vector bundle over B, which we denote by F. (All vector bundles here are algebraic.) A G-vector bundle over B is called trivial if it is isomorphic to F for some G-module F . From the endomorphism ring R of ...

Analytic Cycles and Vector Bundles on Non-Compact Algebraic Varieties*

A. Orders of Growth on Algebraic Varieties . . . . . . . . . . . 4 w 1. Review of the Classical Theory . . . . . . . . . . . . . 4 w 2. Generalization to Algebraic Varieties . . . . . . . . . . . 6 w 3. Exhaustion Functions and K~ihler Metrics on Special Affine Varieties . . . . . . . . . . . . . . . . . . . . . . . 9 84. Order of Growth of Analytic Sets . . . . . . . . . . . . 13 w 5. Order of...

Exact sequences of semistable vector bundles on algebraic curves

Let X be a smooth complex projective curve of genus g ≥ 1. If g ≥ 2, assume further that X is either bielliptic or with general moduli. Fix integers r, s, a, b with r > 1, s > 1 and as ≤ br. Here we prove the existence of an exact sequence 0 → H → E → Q → 0 of semistable vector bundles onX with rk(H) = r, rk(Q) = s, deg(H) = a and deg(Q) = b.