Segre classes of monomial schemes

TL;DR

This paper presents an explicit formula for computing Segre classes of monomial schemes in nonsingular varieties, using a formal integral over a region defined by the Newton polyhedron, with proofs in two variables and verifications in higher dimensions.

Contribution

It introduces a novel explicit integral formula for Segre classes of monomial schemes, extending understanding of their geometric and algebraic properties.

Findings

Formula proven for monomial ideals in two variables

Verified for certain families in any number of variables

Provides a new computational approach for Segre classes

Abstract

We propose an explicit formula for the Segre classes of monomial subschemes of nonsingular varieties, such as schemes defined by monomial ideals in projective space. The Segre class is expressed as a formal integral on a region bounded by the corresponding Newton polyhedron. We prove this formula for monomial ideals in two variables and verify it for some families of examples in any number of variables.