Vector bundles on a three dimensional neighborhood of a ruled surface

Edoardo Ballico; Elizabeth Gasparim

Vector bundles on a three dimensional neighborhood of a ruled surface

Algebraic Geometry 2007-05-23 v3

Authors: Edoardo Ballico , Elizabeth Gasparim

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.

Cite

@article{arxiv.math/0110258,
  title  = {Vector bundles on a three dimensional neighborhood of a ruled surface},
  author = {Edoardo Ballico and Elizabeth Gasparim},
  journal= {arXiv preprint arXiv:math/0110258},
  year   = {2007}
}

Comments

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

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