Chern Numbers of Smooth Varieties via Homotopy Continuation and Intersection Theory

Details Chern Numbers of Smooth Varieties via Homotopy Continuation and Intersection Theory Chern Numbers of Smooth Varieties via Homotopy Continuation and Intersection Theory

2009-09-11

arxiv.org/abs/0909.2111v1

Mathematics

Algebraic Geometry

Scientific paper

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 P^n. We illustrate the approach through several worked examples.

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