Real and complex indices of vector fields on complete intersection curves with isolated singularity
摘要
If (V,0) is an isolated complete intersection singularity and X a holomorphic vector field tangent to V one can define an index of X, the so called GSV index, which generalizes the Poincare-Hopf index. We prove that the GSV index coincides with the dimension of a certain explicitely constructed vector space, if X is deformable in a certain sense and V is a curve. We also give a sufficient algebraic criterion for X to be deformable in this way. If one considers the real analytic case one can also define an index of X which is called the real GSV index. Under the condition that X has the deformation property, we prove a signature formula for the index generalizing the Eisenbud-Levine Theorem.
引用
@article{arxiv.math/0301166,
title = {Real and complex indices of vector fields on complete intersection curves with isolated singularity},
author = {Oliver Klehn},
journal= {arXiv preprint arXiv:math/0301166},
year = {2007}
}
备注
Major revision. Main changes are the corrections of the statements and proofs of the main theorems. 16 pages, to appear in Compositio Mathematica