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Computing Segre classes in arbitrary projective varieties

Harris, Corey

Journal of symbolic computation, 2017-09, Vol.82, p.26-37 [Revista revisada por pares]

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Título:
Computing Segre classes in arbitrary projective varieties
Autor: Harris, Corey
Materias: Characteristic class ; Chern–Mather class ; Chern–Schwartz–MacPherson class ; Computational algebraic geometry ; Euclidean distance degree ; Intersection theory ; Macaulay2 ; Segre class
Es parte de: Journal of symbolic computation, 2017-09, Vol.82, p.26-37
Descripción: 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.
Editor: Elsevier Ltd
Idioma: Inglés

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