Vector Bundles on a Neighborhood of an Exceptional Curve and Elementary Transformations

Details Vector Bundles on a Neighborhood of an Exceptional Curve and Elementary Transformations Vector Bundles on a Neighborhood of an Exceptional Curve and Elementary Transformations

2001-08-21

arxiv.org/abs/math/0108146v1

Mathematics

Algebraic Geometry

To appear in Forum Mathematicum

Scientific paper

Let W be the germ of a smooth complex surface around an exceptional curve and let E be a rank 2 vector bundle on W. We study the cohomological properties of a finite sequence $E_i, 1 \leq i \leq t$ of rank 2 vector bundles canonically associated to E. We calculate numerical invariants of E in terms of the $E_i.$ If S is a compact complex smooth surface and E is a rank 2 bundle on the blow- up of S at a point, we show that all values of $c_2(E)-c_2(\pi_* E^{\vee\vee})$ that are numerically possible are actually attained.

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