Segre Class Computation and Practical Applications

Abstract

Let $X\subset Y$ be closed (possibly singular) subschemes of a smooth projective toric variety $T$. We show how to compute the Segre class $s(X,Y)$ as a class in the Chow group of $T$. Building on this, we give effective methods to compute intersection products in projective varieties, to determine algebraic multiplicity without working in local rings, and to test pairwise containment of subvarieties of $T$. Our methods may be implemented without using Groebner bases; in particular any algorithm to compute the number of solutions of a zero-dimensional polynomial system may be used.

References in corpus (5)

• Computing characteristic classes of projective schemes
• An Algorithm to Compute the Topological Euler Characteristic, Chern-Schwartz-MacPherson Class and Segre Class of Projective Varieties
• The Chern-Schwartz-MacPherson class of an embeddable scheme
• Computing characteristic classes of subschemes of smooth toric varieties
• Computations over Local Rings in Macaulay2

Cited by in corpus (6)

• Conormal Spaces and Whitney Stratifications
• Maximum Likelihood Estimation of Toric Fano Varieties
• The Maximum Likelihood Degree of Linear Spaces of Symmetric Matrices
• Segre classes and invariants of singular varieties
• Probabilistic Saturations and Alt's Problem
• Applications of intersection theory: from maximum likelihood to chromatic polynomials