Segre class computation and practical applications

Harris, Corey; Helmer, Martin

doi:10.1090/mcom/3448

Segre class computation and practical applications
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by Corey Harris and Martin Helmer;

Math. Comp. 89 (2020), 465-491

DOI: https://doi.org/10.1090/mcom/3448

Published electronically: May 24, 2019

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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 Gröbner bases; in particular any algorithm to compute the number of solutions of a zero-dimensional polynomial system may be used.

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