English

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}
}