Computing Segre classes in arbitrary projective varieties. (September 2017)

• Record Type: Journal Article
• Authors: Harris, Corey
• Is Part Of: Journal of symbolic computation. Volume 82(2017)
• Page Start: 26
• Page End: 37
• Publication Date: 2017-09
• Subjects: Intersection theory -- Segre class -- Chern–Mather class -- Chern–Schwartz–MacPherson class -- Characteristic class -- Euclidean distance degree -- Computational algebraic geometry -- Macaulay2; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2016.09.003
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We give an algorithm for computing Segre classes of subschemes of arbitrary projective varieties by computing degrees of a sequence of linear projections. Based on the fact that Segre classes of projective varieties commute with intersections by general effective Cartier divisors, we can compile a system of linear equations which determine the coefficients for the Segre class pushed forward to projective space. The algorithm presented here comes after several others which solve the problem in special cases, where the ambient variety is for instance projective space; to our knowledge, this is the first algorithm to be able to compute Segre classes in projective varieties with arbitrary singularities.