Bivariant Chern classes for morphisms with nonsingular target varieties

Shoji Yokura

Open Mathematics (2005)

  • Volume: 3, Issue: 4, page 614-626
  • ISSN: 2391-5455

Abstract

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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 𝔽 ˜ of constructible functions and a unique bivariant Chern class γ: 𝔽 ˜ → ℍ .

How to cite

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Shoji Yokura. "Bivariant Chern classes for morphisms with nonsingular target varieties." Open Mathematics 3.4 (2005): 614-626. <http://eudml.org/doc/268871>.

@article{ShojiYokura2005,
abstract = {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: \[\tilde\{\mathbb \{F\}\} \rightarrow \{\mathbb \{H\}\}\] .},
author = {Shoji Yokura},
journal = {Open Mathematics},
keywords = {14C17; 14F99; 55N35},
language = {eng},
number = {4},
pages = {614-626},
title = {Bivariant Chern classes for morphisms with nonsingular target varieties},
url = {http://eudml.org/doc/268871},
volume = {3},
year = {2005},
}

TY - JOUR
AU - Shoji Yokura
TI - Bivariant Chern classes for morphisms with nonsingular target varieties
JO - Open Mathematics
PY - 2005
VL - 3
IS - 4
SP - 614
EP - 626
AB - 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: \[\tilde{\mathbb {F}} \rightarrow {\mathbb {H}}\] .
LA - eng
KW - 14C17; 14F99; 55N35
UR - http://eudml.org/doc/268871
ER -

References

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