Vector bundles near negative curves: moduli and local Euler characteristic

Abstract

We study moduli spaces of vector bundles on a two-dimensional neighbourhood $Z_k$ of an irreducible curve $\ell =C{P}^1$ with ${\ell }^2=-k$ 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/ .

final version

References in corpus (2)

• La correspondance de McKay
• Three Applications of Instanton Numbers

Cited by in corpus (11)

• The Nekrasov Conjecture for Toric Surfaces
• Local moduli of holomorphic bundles
• Quantizations of local surfaces and rebel instantons
• Moduli Stacks of Bundles on Local Surfaces
• Classical deformations of noncompact surfaces and their moduli of instantons
• Isomorphisms of Moduli Spaces
• Curvature Grafted by Instantons
• Infinite dimensional families of Calabi-Yau threefolds and moduli of vector bundles
• Intrinsic mirrors for minimal adjoint orbits and categories of singularities
• Deformations of noncompact Calabi--Yau manifolds, families and diamonds
• Some contributions of Edoardo Ballico to Moduli spaces and their applications