Chern numbers of smooth varieties via homotopy continuation and intersection theory

Authors:
Sandra Di Rocco;David Eklund;Chris Peterson;Andrew J. Sommese
Affiliations:
Department of Mathematics, KTH, 100 44 Stockholm, Sweden;Department of Mathematics, KTH, 100 44 Stockholm, Sweden;Department of Mathematics, Colorado State University, Fort Collins, CO 80523, United States;Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, United States
Venue:
Journal of Symbolic Computation
Year:
2011

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