Chern numbers of smooth varieties via homotopy continuation and intersection theory

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• 作者：S ; ra Di Rocco ; David Eklund ; Chris Peterson ; Andrew J. Sommese
• 关键词：Homotopy continuation ; Numerical algebraic geometry ; Polynomial system ; Linear system ; Linkage ; Curve ; Surface
• 刊名：Journal of Symbolic Computation
• 出版年：2011
• 出版时间：January 2011
• 年：2011
• 卷：46
• 期：1
• 页码：23-33
• 全文大小：256 K

文摘

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 . We illustrate the approach through several worked examples.