Newton-Okounkov bodies and Segre classes [article]

Paolo Aluffi
2018 arXiv   pre-print
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.
arXiv:1809.07344v1 fatcat:v453zp4ci5dyvbphqil2g6r2rm