Local holomorphic Euler characteristic and instanton decay

Details Local holomorphic Euler characteristic and instanton decay Local holomorphic Euler characteristic and instanton decay

2007-09-17

arxiv.org/abs/0709.2577v2

Pure Appl. Math. Q. 4 no. 2, Special Issue: In honor of Fedya Bogomolov, Part 1, 161-179 (2008)

Mathematics

Algebraic Geometry

15 pages. Revision history: v1: Original. v2: minor corrections, as published

Scientific paper

We study the local holomorphic Euler characteristic $\chi(x,\mathcal{F})$ of sheaves near a surface singularity obtained from contracting a line $\ell$ inside a smooth surface $Z$. We prove non-existence of sheaves with certain prescribed numerical invariants. Non-existence of instantons on $Z$ with certain charges follows, and we conclude that $\ell^2$ poses an obstruction to instanton decay. A Macaulay 2 algorithm to compute $\chi$ is made available at http://www.maths.ed.ac.uk/~s0571100/Instanton/

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