Complex Links and Algebraic Multiplicities
Year: 2020
Type: preprint
Abstract: This paper is concerned with two invariants associated to pairs of strata $X < Y$ in an analytic stratification of some ambient complex projective variety $W$. We show that if the closures $\overline{X} \subset \overline{Y}$ are subvarieties of $W$ with $\overline{X}$ irreducible, then the Hilbert-Samuel multiplicity of $\overline{Y}$ along $\overline{X}$ equals the Euler characteristic of the space obtained by intersecting $Y$ with the complex link of $X$ in $W$. En route, we obtain a local Lefschetz hyperplane theorem for such complex linking spaces. Applications of this result include a new algebraic formula for the Euler obstruction of $W$.
Source: arXiv (Cornell University)
Authors: Martin Helmer, Vidit Nanda
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3036819444