Vector bundles near negative curves: moduli and local Euler characteristic

Edoardo Ballico; Elizabeth Gasparim; Thomas Köppe

doi:10.1080/00927870802562351

paper

Vector bundles near negative curves: moduli and local Euler characteristic

arXiv:math/0404012 · doi:10.1080/00927870802562351

Abstract

We study moduli spaces of vector bundles on a two-dimensional neighbourhood $Z_{k}$ of an irreducible curve $ℓ = C P^{1}$ with $ℓ^{2} = - k$ and give an explicit construction of these moduli as stratified spaces. We give sharp bounds for the local holomorphic Euler characteristic of bundles on $Z_{k}$ and prove existence of families of bundles with prescribed numerical invariants. Our numerical calculations are performed using a Macaulay 2 algorithm, which is available for download at http://www.maths.ed.ac.uk/~s0571100/Instanton/ .

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