Segre classes as integrals over polytopes
Algebraic Geometry
2021-02-08 v2
Abstract
We express the Segre class of a monomial scheme -- or, more generally, a scheme monomially supported on a set of divisors cutting out complete intersections -- in terms of an integral computed over an associated body in euclidean space. The formula is in the spirit of the classical Bernstein-Kouchnirenko theorem computing intersection numbers of equivariant divisors in a torus in terms of mixed volumes, but deals with the more refined intersection-theoretic invariants given by Segre classes, and holds in the less restrictive context of `r.c. monomial schemes'.
Cite
@article{arxiv.1307.0830,
title = {Segre classes as integrals over polytopes},
author = {Paolo Aluffi},
journal= {arXiv preprint arXiv:1307.0830},
year = {2021}
}