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

Edoardo Ballico·Elizabeth Gasparim
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Abstract

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 $c_2(E)-c_2(π_* E^{\vee\vee})$ that are numerically possible are actually attained.

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Edoardo Ballico, Elizabeth Gasparim. 2001-08-21. Vector Bundles on a Neighborhood of an Exceptional Curve and Elementary Transformations. https://arxiv.org/abs/math/0108146

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