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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
  • University of Kagoshima

Bibliografia

  • [1] J.-P. Brasselet: “Existence des classes de Chern en théorie bivariante”, Astérisque, Vol. 101–102, (1981), pp. 7–22.
  • [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.
  • [4] N. Chriss and V. Ginzburg: Representation theory and complex geometry, Birkhäuser, 1997.
  • [5] A. Dimca: Sheaves in Topology, Springer-Verlag, 2004.
  • [6] W. Fulton: Intersection Theory, Springer-Verlag, 1984.
  • [7] W. Fulton and R. MacPherson: “Categorical frameworks for the study of singular spaces”, Memoirs of Amer. Math. Soc., Vol. 243, (1981).
  • [8] V. Ginzburg: “G-Modules, Springer’s Representations and Bivariant Chern Classes”, Adv. in Maths., Vol. 61, (1986), pp. 1–48. http://dx.doi.org/10.1016/0001-8708(86)90064-2
  • [9] V. Ginzburg: “Geometric methods in the representation theory of Hecke algebras and quantum groups”, In: A. Broer and A. Daigneault (Eds.): Representation theories and algebraic geometry (Montreal, PQ, 1997), Kluwer Acad. Publ., Dordrecht, 1998, pp. 127–183.
  • [10] M. Kashiwara and P. Schapira: Sheaves on Manifolds, Springer-Verlag, 1990.
  • [11] G. Kennedy: “MacPherson’s Chern classes of singular algebraic varieties”, Comm. Algebra, Vol. 9 (18), (1990), pp. 2821–2839.
  • [12] M. Kwieciński: “Formule du produit pour les classes caractéristiques deChern-Schwartz-MacPherson et homologie d’intersection”, C. R. Acad. Sci. Paris, Vol. 314, (1992) pp. 625–628.
  • [13] M. Kwieciński: “Sur le transformé de Nash et la construction du graph de MacPherson”, In: Thèse, Université de Provence, 1994.
  • [14] M. Kwieciński and S. Yokura: “Product formula of the twisted MacPherson class”, Proc. Japan Acad., Vol. 68, (1992) pp. 167–171.
  • [15] R. MacPherson: “Chern classes for singular algebraic varieties”, Ann. of Math., Vol. 100, (1974), pp. 423–432. http://dx.doi.org/10.2307/1971080
  • [16] C. Sabbah: Espaces conormaux bivariants, Thèse, l’Université Paris, Vol. 7, 1986.
  • [17] P. Schapira: “Operations on constructible functions”, J. Pure Appl. Algebra, Vol. 72, (1991), pp. 83–93. http://dx.doi.org/10.1016/0022-4049(91)90131-K
  • [18] J. Schürmann: “A generalized Verdier-type Riemann-Roch theorem for Chern-Schwartz Mac-Pherson classes”, math. AG/0202175.
  • [19] J. Schürmann: “A general construction of partial Grothendieck transformations”, math. AG/0209299.
  • [20] J. Schürmann: Topology of singular spaces and constructible sheaves, Monografie Matematyczne, Vol. 63, (New Series), Birkhäuser, Basel, 2003.
  • [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.
  • [22] M.-H. Schwartz: “Classes et caractères de Chern des espaces linéaires”, Pub. Int. Univ. Lille, 2 Fasc. 3, (1980).
  • [23] O. Viro: “Some integral calculus based on the Euler characteristic”, Springer Lect. Notes Math., Vol. 1346, (1989), pp. 127–138. http://dx.doi.org/10.1007/BFb0082775
  • [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
  • [27] J. Zhou: Classes de Chern en théorie bivariante, Thèse, Université Aix-Marseille, Vol. 2, 1995.
  • [28] J. Zhou: “Morphisme cellulaire et classes de Chern bivariantes”, Ann. Fac. Sci. Toulouse Math., Vol. 9, (2000), pp. 161–192.

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Bibliografia

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