Segre class computation and practical applications

Harris, Corey; Helmer, Martin

doi:10.1090/mcom/3448

Segre class computation and practical applications

Authors: Corey Harris and Martin Helmer
Journal: Math. Comp. 89 (2020), 465-491
MSC (2010): Primary 14Qxx, 13Pxx, 13H15, 14C17, 14C20, 68W30, 65H10
DOI: https://doi.org/10.1090/mcom/3448
Published electronically: May 24, 2019
MathSciNet review: 4011552
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Abstract: Let $X \subset Y$ be closed (possibly singular) subschemes of a smooth projective toric variety . We show how to compute the Segre class as a class in the Chow group of . 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 . 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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