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Vector fields on some class of complete symmetric varieties

Published online by Cambridge University Press:  22 January 2016

Yoshifumi Kato
Yoshifumi Kato*
Affiliation:
Department of Mathematical Engineering, Faculty of Engineering, Nagoya University Chikusa-ku, Nagoya 464, Japan
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In the previous papers [6], [7], we show that the set of an algebraic homogeneous space G/P fixed under the action of a maximal torus T can be canonically identified with the coset W1 = W/W1 of Weyl group W. We find a T invariant Zariski open set near each element w ∊ W1 and introduce a very nice local coordinate system such that we can express the maximal torus action explicitly. As a result, we become able to apply the study of J. B. Carrell and D. Lieberman [2], [3] to the space G/P and investigate the numerical properties of its characteristic classes and cycles.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 103 , October 1986 , pp. 85 - 94
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1986

References

[1] Bialynicki-Birula, , Some theorems on actions of algebraic groups, Ann. of Math., 98 (1973), 480–497.CrossRefGoogle Scholar
[2] Carrell, J. B., Chern classes of the Grassmannians and Schubert calculus, Topology, 17 (1978),177–182.Google Scholar
[3] Carrell, J. B. and Lieberman, D., Vector fields and Chern numbers, Math. Ann., 225 (1977), 263–273.Google Scholar
[4] DeConcini, C. and Procesi, C., Complete symmetric varieties, Springer Lect. Notes, 996, 1–44.Google Scholar
[5] DeConcini, C. and Procesi, C., Complete symmetric varieties II (Intersection theory), Preprint.Google Scholar
[6] Kato, Y., A new characterization of the Bruhat decomposition, Nagoya Math. J., 86 (1982), 131–153.CrossRefGoogle Scholar
[7] Kato, Y., On the vector fields on an algebraic homogeneous space, Pacific J. of Math., 108 (1983), 285–294.Google Scholar
[8] Kosniowsky, C., Applications of the holomorphic Lefschetz formulae, Bull. London Math. Soc, 2 (1970), 43–48.CrossRefGoogle Scholar
[9] Sommese, A. J., Holomorphic vector fields on compact kähler manifolds, Math. Ann., 210 (1974), 75–82.Google Scholar