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arXiv · 1809.07344

Newton-Okounkov bodies and Segre classes

Paolo Aluffi
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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.

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Paolo Aluffi. 2018-09-19. Newton-Okounkov bodies and Segre classes. https://doi.org/10.1353/ajm.2021.0038

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