Segre classes as integrals over polytopes

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'.

References in corpus (2)

• Multidegrees of monomial rational maps
• Log canonical threshold, Segre classes, and polygamma functions

Cited by in corpus (11)

• Gromov-Witten theory with maximal contacts
• The Maximum Likelihood Degree of Linear Spaces of Symmetric Matrices
• A case study of intersections on blowups of the moduli of curves
• The Segre zeta function of an ideal
• Virtual classes for the working mathematician
• Lorentzian polynomials, Segre classes, and adjoint polynomials of convex polyhedral cones
• Tensored Segre classes
• Multidegrees of monomial rational maps
• Log canonical threshold, Segre classes, and polygamma functions
• Newton-Okounkov bodies and Segre classes
• Combinatorial Excess Intersection