Vector bundles on a three dimensional neighborhood of a ruled surface

Abstract

Let $S$ be a ruled surface inside a smooth threefold $W$ and let $E$ be a vector bundle on a formal neighborhood of $S.$ We find minimal conditions under which the local moduli space of $E$ is finite dimensional and smooth. Moreover, we show that $E$ is a flat limit of a flat family of vector bundles whose general element we describe explicitly.

Revised version to appear in J. Pure Appl. Algebra. A new section on deformations was added