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2005 | 3 | 4 | 614-626
Tytuł artykułu

Bivariant Chern classes for morphisms with nonsingular target varieties

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Języki publikacji
EN
Abstrakty
EN
W. Fulton and R. MacPherson posed the problem of unique existence of a bivariant Chern class-a Grothendieck transformation from the bivariant theory F of constructible functions to the bivariant homology theory H. J.-P. Brasselet proved the existence of a bivariant Chern class in the category of embeddable analytic varieties with cellular morphisms. In general however, the problem of uniqueness is still unresolved. In this paper we show that for morphisms having nonsingular target varieties there exists another bivariant theory $$\tilde {\mathbb{F}}$$ of constructible functions and a unique bivariant Chern class γ: $$\tilde {\mathbb{F}} \to {\mathbb{H}}$$ .
Wydawca
Czasopismo
Rocznik
Tom
3
Numer
4
Strony
614-626
Opis fizyczny
Daty
wydano
2005-12-01
online
2005-12-01
Twórcy
autor
Bibliografia
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  • [2] J.-P. Brasselet, J. Schürmann and S. Yokura: “Bivariant Chern classes and Grothendieck transformations”, Math. AG/0404132.
  • [3] J.-P. Brasselet and M.-H. Schwartz: “Sur les classes de Chern d’un ensemble analytique complexe”, Astérisque, Vol. 82–83, (1981), pp. 93–148.
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  • [21] M.-H. Schwartz: “Classes caractéristiques définies par une stratification d’unevariété analytique complexe”, C. R. Acad. Sci. Paris, Vol. 260, (1965), pp. 3262–3264, 3535–3537.
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  • [24] S. Yokura: “On a Verdier-type Riemann-Roch for Chern-Schwartz-MacPherson class”, Topology and Its Applications, Vol. 94, (1999), pp. 315–327. http://dx.doi.org/10.1016/S0166-8641(98)00037-6
  • [25] S. Yokura: “On the uniqueness problem of the bivariant Chern classes”, Documenta Mathematica, Vol. 7, (2002), pp. 133–142.
  • [26] S. Yokura: “Bivariant theories of constructible functions and Grothendieck transformations”, Topology and Its Applications, Vol. 123, (2002), pp. 283–296. http://dx.doi.org/10.1016/S0166-8641(01)00197-3
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Typ dokumentu
Bibliografia
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bwmeta1.element.doi-10_2478_BF02475622
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