Chern numbers of smooth varieties via homotopy continuation and intersection theory

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.

• Type: Journal
• Year: 2011
• Where: JSC
• Authors: Sandra Di Rocco, David Eklund, Chris Peterson, Andrew J. Sommese
• Keywords: Chern Classes, Intersection Product, JSC 2011, Smooth Variety