Euler characteristic of a mixed Koszul complex and the index of vector fields

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.

Publication Details

Journal
ArXiv.org
Published
2025-09-04
Primary Topic
Geochemistry and Geologic Mapping
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

Euler characteristic of a mixed Koszul complex and the index of vector fields

ArXiv.org
Geochemistry and Geologic Mapping
article

Euler characteristic of a mixed Koszul complex and the index of vector fields

article en

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.

ArXiv.org
Openalex Percentile: Top 48%
Geochemistry and Geologic Mapping
Open Access PDFOpenAlex
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Euler characteristic of a mixed Koszul complex and the index of vector fields · ArXiv.org (2025) | TGRS Research Map | TGRS