Computing Segre classes in arbitrary projective varieties. 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.
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References in zbMATH (referenced in 8 articles , 1 standard article )
Showing results 1 to 8 of 8.
- Harris, Corey; Helmer, Martin: Segre class computation and practical applications (2020)
- Achilles, R.; Manaresi, M.; Pruschke, T.: Mixed multiplicities, Segre numbers and Segre classes (2019)
- Aluffi, Paolo: Projective duality and a Chern-Mather involution (2018)
- Di Rocco, Sandra; Eklund, David; Peterson, Chris: Numerical polar calculus and cohomology of line bundles (2018)
- Aluffi, Paolo: The Segre zeta function of an ideal (2017)
- Giovanni Stagliano: A Macaulay2 package for computations with rational maps (2017) arXiv
- Harris, Corey: Computing Segre classes in arbitrary projective varieties (2017)
- Helmer, Martin: Computing characteristic classes of subschemes of smooth toric varieties (2017)