CharacteristicClasses -- Chern classes and other characteristic classes of subschemes of certain smooth toric varieties, including products of projective spaces. The package CharacteristicClasses provides commands to compute the Chern class, Chern-Schwartz-MacPherson class Segre class and Euler characteristic of closed subschemes of certain smooth complete varieties, including products of projective spaces ℙn1 x ... x ℙnm. In particular the methods of this package are applicable for toric varieties for which all Cartier divisors are numerically effective (nef), see [7] for details. For simplicity a method (CheckToricVarietyValid) is provided which allows the user to determine if these methods can be applied to a given object of class NormalToricVariety. Note that to perform computations involving toric varieties it is required that the package NormalToricVarieties is also loaded.

References in zbMATH (referenced in 16 articles , 2 standard articles )

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  1. Harris, Corey; Helmer, Martin: Segre class computation and practical applications (2020)
  2. Jorgenson, Grayson: A relative Segre zeta function (2020)
  3. Achilles, R.; Manaresi, M.; Pruschke, T.: Mixed multiplicities, Segre numbers and Segre classes (2019)
  4. Aluffi, Paolo: The Chern-Schwartz-MacPherson class of an embeddable scheme (2019)
  5. Bitoun, Thomas; Bogner, Christian; Klausen, René Pascal; Panzer, Erik: Feynman integral relations from parametric annihilators (2019)
  6. Cachazo, Freddy; Early, Nick; Guevara, Alfredo; Mizera, Sebastian: Scattering equations: from projective spaces to tropical Grassmannians (2019)
  7. Fullwood, James; Helmer, Martin: On the Euler characteristic of a relative hypersurface (2019)
  8. Aluffi, Paolo: The Segre zeta function of an ideal (2017)
  9. Giovanni Stagliano: A Macaulay2 package for computations with rational maps (2017) arXiv
  10. Harris, Corey: Computing Segre classes in arbitrary projective varieties (2017)
  11. Helmer, Martin: A direct algorithm to compute the topological Euler characteristic and Chern-Schwartz-MacPherson class of projective complete intersection varieties (2017)
  12. Helmer, Martin: Computing the Chern-Schwartz-MacPherson Class of complete simplical toric varieties (2017)
  13. Helmer, Martin: Computing characteristic classes of subschemes of smooth toric varieties (2017)
  14. Helmer, Martin: Algorithms to compute the topological Euler characteristic, Chern-Schwartz-MacPherson class and Segre class of projective varieties (2016)
  15. Jost, Christine: Computing characteristic classes and the topological Euler characteristic of complex projective schemes (2015)
  16. Rossmann, Tobias: Computing topological zeta functions of groups, algebras, and modules. II. (2015)