Chern classes of reductive groups and an adjunction formula

Valentina Kiritchenko[1]

  • [1] State University of New York at Stony Brook Dept. of Mathematics

Annales de l’institut Fourier (2006)

  • Volume: 56, Issue: 4, page 1225-1256
  • ISSN: 0373-0956

Abstract

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In this paper, I construct noncompact analogs of the Chern classes for equivariant vector bundles over complex reductive groups. For the tangent bundle, these Chern classes yield an adjunction formula for the (topological) Euler characteristic of complete intersections in reductive groups. In the case where a complete intersection is a curve, this formula gives an explicit answer for the Euler characteristic and the genus of the curve. I also prove that the higher Chern classes vanish. The first and the last nontrivial Chern classes are described explicitly. An extension of these results to the setting of spherical homogeneous spaces is outlined.

How to cite

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Kiritchenko, Valentina. "Chern classes of reductive groups and an adjunction formula." Annales de l’institut Fourier 56.4 (2006): 1225-1256. <http://eudml.org/doc/10171>.

@article{Kiritchenko2006,
abstract = {In this paper, I construct noncompact analogs of the Chern classes for equivariant vector bundles over complex reductive groups. For the tangent bundle, these Chern classes yield an adjunction formula for the (topological) Euler characteristic of complete intersections in reductive groups. In the case where a complete intersection is a curve, this formula gives an explicit answer for the Euler characteristic and the genus of the curve. I also prove that the higher Chern classes vanish. The first and the last nontrivial Chern classes are described explicitly. An extension of these results to the setting of spherical homogeneous spaces is outlined.},
affiliation = {State University of New York at Stony Brook Dept. of Mathematics},
author = {Kiritchenko, Valentina},
journal = {Annales de l’institut Fourier},
keywords = {Reductive groups; hyperplane section; Chern classes; complex reductive groups; representations; affine hyperplane sections; regular compactifications; spherical varieties},
language = {eng},
number = {4},
pages = {1225-1256},
publisher = {Association des Annales de l’institut Fourier},
title = {Chern classes of reductive groups and an adjunction formula},
url = {http://eudml.org/doc/10171},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Kiritchenko, Valentina
TI - Chern classes of reductive groups and an adjunction formula
JO - Annales de l’institut Fourier
PY - 2006
PB - Association des Annales de l’institut Fourier
VL - 56
IS - 4
SP - 1225
EP - 1256
AB - In this paper, I construct noncompact analogs of the Chern classes for equivariant vector bundles over complex reductive groups. For the tangent bundle, these Chern classes yield an adjunction formula for the (topological) Euler characteristic of complete intersections in reductive groups. In the case where a complete intersection is a curve, this formula gives an explicit answer for the Euler characteristic and the genus of the curve. I also prove that the higher Chern classes vanish. The first and the last nontrivial Chern classes are described explicitly. An extension of these results to the setting of spherical homogeneous spaces is outlined.
LA - eng
KW - Reductive groups; hyperplane section; Chern classes; complex reductive groups; representations; affine hyperplane sections; regular compactifications; spherical varieties
UR - http://eudml.org/doc/10171
ER -

References

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