Bivariant Chern-Schwartz-MacPherson classes with values in Chow groups

• L. Ernström ^[1] ; S. Yokura ^[2]
  1. [1] Royal Institute of Technology

     Royal Institute of Technology

     Suecia

     
  2. [2] University of Kagoshima, Japón
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 8, Nº. 1, 2002, págs. 1-25
• Idioma: inglés
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• Resumen

  • Fulton and MacPherson asked if there exists a bivariant version of the Chern-Schwartz-MacPherson class. Brasselet solved this problem affirmatively in the category of analytic varieties and cellular morphisms. However, it has not been solved in the general case and the uniqueness of such a bivariant Chern class is still open. In this paper we show the unique existence of the bivariant Chern-Schwartz-MacPherson class with values in Chow groups. To be more precise, we show that there exists a unique Grothendieck transformation from the bivariant theory of constructible functions to Fulton-MacPherson's operational bivariant theory of Chow groups, provided that the compatibility with flat pullback is not required on the operational bivariant theory.