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Chern numbers of smooth varieties via homotopy continuation and intersection theory. (English) Zbl 1200.14014

Summary: 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 \(\mathbb P^n\). We illustrate the approach through several worked examples.

MSC:

14C15 (Equivariant) Chow groups and rings; motives
14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
14M07 Low codimension problems in algebraic geometry
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