The index of a real vector field at an isolated complete intersection singularity
Algebraic Geometry
2025-08-28 v1
Abstract
In an unpublished note [H1] we have described a method to obtain a formula for the index of an analytic vector field with (complex) isolated zero on a real analytic hypersurface with (complex) isolated singularity. This formula, like the one of Eisenbud-Levine and Khimshiashvili [AGV] for smooth points, expresses the index by the signature of bilinear forms, which are defined by a local residue symbol (cf. [Ma]). In the complete intersection case, we use a generalized residue symbol, defined for free resolutions in [LJ], in the special case of generalized Koszul complexes to obtain a suitable calculus for the bilinear forms involved.
Cite
@article{arxiv.2508.19718,
title = {The index of a real vector field at an isolated complete intersection singularity},
author = {Achim Hennings},
journal= {arXiv preprint arXiv:2508.19718},
year = {2025}
}