Chern Numbers of Smooth Varieties via Homotopy Continuation and Intersection Theory

2009/09/11 by Sandra Di Rocco, David Eklund, Di Rocco, Sandra +5
Computer Science · Mathematics · #13Dxx #13Pxx #14M06 #14Qxx #65E05 #65H10 #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.0909.2111

openalex publication_date 2009/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Homotopy continuation provides a numerical tool for computing the equivalence of a smooth variety in an intersection product. Intersection theory provides a theoretical tool for relating the equivalence of a smooth variety in an intersection product to the degrees of the Chern classes of the variety. A combination of these tools leads to a numerical method for computing the degrees of Chern classes of smooth projective varieties in Pⁿ. We illustrate the approach through several worked examples.

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