An algebraic formula for the index of a vector field on an isolated complete intersection singularity
Algebraic Geometry
2009-07-10 v3 Commutative Algebra
Abstract
Let (V,0) be a germ of a complete intersection variety in \CC^{n+k}, n>0, having an isolated singularity at 0 and X be the germ of a holomorphic vector field on \CC^{n+k} tangent to V and having on V an isolated zero at 0. We show that in this case the homological index and the GSV-index coincide. In the case when the zero of X is also isolated in the ambient space \CC^{n+k} we give a formula for the homological index in terms of local linear algebra.
Keywords
Cite
@article{arxiv.math/0601640,
title = {An algebraic formula for the index of a vector field on an isolated complete intersection singularity},
author = {H. -Chr. Graf von Bothmer and W. Ebeling and X. Gomez-Mont},
journal= {arXiv preprint arXiv:math/0601640},
year = {2009}
}
Comments
18 pages; added an example which is not quasi homogeneous. A script calculating this example can be found at http://www.iag.uni-hannover.de/~bothmer/gobelin/ or at the and of the source file of this article