Uniqueness of equivariant singular Bott-Chern classes

Shun Tang[1]

  • [1] Université Paris-Sud Département de Mathématiques Bâtiment 425 91405 Orsay cedex (France)

Annales de l’institut Fourier (2012)

  • Volume: 62, Issue: 4, page 1437-1482
  • ISSN: 0373-0956

Abstract

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In this paper, we shall discuss possible theories of defining equivariant singular Bott-Chern classes and corresponding uniqueness property. By adding a natural axiomatic characterization to the usual ones of equivariant Bott-Chern secondary characteristic classes, we will see that the construction of Bismut’s equivariant Bott-Chern singular currents provides a unique way to define a theory of equivariant singular Bott-Chern classes. This generalizes J. I. Burgos Gil and R. Liţcanu’s discussion to the equivariant case. As a byproduct of this study, we shall prove a concentration formula which can be used to prove an arithmetic concentration theorem in Arakelov geometry.

How to cite

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Tang, Shun. "Uniqueness of equivariant singular Bott-Chern classes." Annales de l’institut Fourier 62.4 (2012): 1437-1482. <http://eudml.org/doc/251137>.

@article{Tang2012,
abstract = {In this paper, we shall discuss possible theories of defining equivariant singular Bott-Chern classes and corresponding uniqueness property. By adding a natural axiomatic characterization to the usual ones of equivariant Bott-Chern secondary characteristic classes, we will see that the construction of Bismut’s equivariant Bott-Chern singular currents provides a unique way to define a theory of equivariant singular Bott-Chern classes. This generalizes J. I. Burgos Gil and R. Liţcanu’s discussion to the equivariant case. As a byproduct of this study, we shall prove a concentration formula which can be used to prove an arithmetic concentration theorem in Arakelov geometry.},
affiliation = {Université Paris-Sud Département de Mathématiques Bâtiment 425 91405 Orsay cedex (France)},
author = {Tang, Shun},
journal = {Annales de l’institut Fourier},
keywords = {uniqueness; equivariant; singular Bott-Chern classes; singular Bott-Chern forms; Riemann-Roch; equivariant secondary classes; axiomatic for Bott-Chern forms},
language = {eng},
number = {4},
pages = {1437-1482},
publisher = {Association des Annales de l’institut Fourier},
title = {Uniqueness of equivariant singular Bott-Chern classes},
url = {http://eudml.org/doc/251137},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Tang, Shun
TI - Uniqueness of equivariant singular Bott-Chern classes
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 4
SP - 1437
EP - 1482
AB - In this paper, we shall discuss possible theories of defining equivariant singular Bott-Chern classes and corresponding uniqueness property. By adding a natural axiomatic characterization to the usual ones of equivariant Bott-Chern secondary characteristic classes, we will see that the construction of Bismut’s equivariant Bott-Chern singular currents provides a unique way to define a theory of equivariant singular Bott-Chern classes. This generalizes J. I. Burgos Gil and R. Liţcanu’s discussion to the equivariant case. As a byproduct of this study, we shall prove a concentration formula which can be used to prove an arithmetic concentration theorem in Arakelov geometry.
LA - eng
KW - uniqueness; equivariant; singular Bott-Chern classes; singular Bott-Chern forms; Riemann-Roch; equivariant secondary classes; axiomatic for Bott-Chern forms
UR - http://eudml.org/doc/251137
ER -

References

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  12. Lars Hörmander, The analysis of linear partial differential operators. I, 256 (1983), Springer-Verlag, Berlin Zbl0521.35001MR717035
  13. Bernhard Köck, The Grothendieck-Riemann-Roch theorem for group scheme actions, Ann. Sci. École Norm. Sup. (4) 31 (1998), 415-458 Zbl0951.14029MR1621405
  14. Kai Köhler, Damian Roessler, A fixed point formula of Lefschetz type in Arakelov geometry. I. Statement and proof, Invent. Math. 145 (2001), 333-396 Zbl0999.14002MR1872550
  15. Pierre Lelong, Intégration sur un ensemble analytique complexe, Bull. Soc. Math. France 85 (1957), 239-262 Zbl0079.30901MR95967
  16. Georges de Rham, Variétés différentiables. Formes, courants, formes harmoniques, (1966), Hermann, Paris Zbl0065.32401
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