Journal of the European Mathematical Society

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Volume 18, Issue 12, 2016, pp. 2849–2863
DOI: 10.4171/JEMS/655

Published online: 2016-11-21

Segre classes as integrals over polytopes

Paolo Aluffi[1]

(1) Florida State University, Tallahassee, USA

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’.

Keywords: Segre classes, monomial ideals, Newton polyhedra

Aluffi Paolo: Segre classes as integrals over polytopes. J. Eur. Math. Soc. 18 (2016), 2849-2863. doi: 10.4171/JEMS/655