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arXiv · 2508.19718

The index of a real vector field at an isolated complete intersection singularity

Achim Hennings
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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In an unpublished note [H1] we have described a method to obtain a formula for the index of an analytic vector field with (complex) isolated zero on a real analytic hypersurface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.

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Achim Hennings. 2025-08-27. The index of a real vector field at an isolated complete intersection singularity. https://arxiv.org/abs/2508.19718

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