Vector bundles on a three dimensional neighborhood of a ruled surface

Details Vector bundles on a three dimensional neighborhood of a ruled surface Vector bundles on a three dimensional neighborhood of a ruled surface

2001-10-23

arxiv.org/abs/math/0110258v3

Mathematics

Algebraic Geometry

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

Scientific paper

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.

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