Euler characteristic of a mixed Koszul complex and the index of vector fields
Commutative Algebra
2025-09-08 v1 Algebraic Geometry
Abstract
A three-term complex of free modules over a local ring determines a mixed Koszul complex, whose Euler characteristic can be expressed by mixed multiplicities. As an application, we offer a simple formula for the index of a holomorphic vector field at an isolated complete intersection singularity.
Keywords
Cite
@article{arxiv.2509.04681,
title = {Euler characteristic of a mixed Koszul complex and the index of vector fields},
author = {Achim Hennings},
journal= {arXiv preprint arXiv:2509.04681},
year = {2025}
}