Newton-Okounkov bodies and Segre classes
Algebraic Geometry
2022-02-11 v1
Abstract
Given a homogeneous ideal in a polynomial ring over C, we adapt the construction of Newton-Okounkov bodies to obtain a convex subset of Euclidean space such that a suitable integral over this set computes the Segre zeta function of the ideal. That is, we extract the numerical information of the Segre class of a subscheme of projective space from an associated (unbounded) Newton-Okounkov convex set. The result generalizes to arbitrary subschemes of projective space the numerical form of a previously known result for monomial schemes.
Cite
@article{arxiv.1809.07344,
title = {Newton-Okounkov bodies and Segre classes},
author = {Paolo Aluffi},
journal= {arXiv preprint arXiv:1809.07344},
year = {2022}
}