## Fixed points of the actions on compact Kähler manifolds.(English)Zbl 0446.53021

### MSC:

 53B35 Local differential geometry of Hermitian and Kählerian structures 32C35 Analytic sheaves and cohomology groups

### Keywords:

Killing vector field; Betti number
Full Text:

### References:

 [1] Bialynicki-Birula, A., Some theorems on actions of algebraic groups, Ann. of Math., 98 (1973), 480-497. · Zbl 0275.14007 [2] Borel, A., Seminar on transformation groups, Ann. of Math. Studies, 46, 1960. · Zbl 0091.37202 [3] , Kahlerian coset spaces of semi-simple Lie groups, Proc. Nat. Acad. Sci. USA, 40 (1954), 1147-1151. · Zbl 0058.16002 [4] Borel, A., Linear algebraic groups, Benjamin, New York, 1969. · Zbl 0186.33201 [5] Borel, A. and Hirzebruch, F., Characteristic classes and homogeneous spaces II, Amer. J. Math., 81 (1959), 315-382. [6] Carrell, J. B. and Lieberman, D. I., Holomorphic vector fields on compact Kahler manifolds, Invent. Math., 21 (1973), 303-309. · Zbl 0253.32017 [7] Deligne, P., Theories de Hodge II, III, Publ. Math. IHES, 40 (1972), 5-57 and 44 (1975), 5-77. [8] Frankel, T. T., Fixed points and torsions on Kahler manifolds, Ann. of Math., 70 (1959), 1-8. · Zbl 0088.38002 [9] Fujiki, A., On automorphism groups of compact Kahler manifolds, Invent. Math., 44 (1978), 225-258. · Zbl 0367.32004 [10] , Duality of mixed Hodge structures of algebraic varieties, to appear in Publ. RIMS, Kyoto Univ. · Zbl 0475.14006 [11] Kaup, W., Reele Transformations Gruppen und invariante Metriken auf komplexen Raumen. Invent. Math., 3 (1967), 43-70. · Zbl 0157.13401 [12] Kobayashi, S., Transformation groups in differential geometry, Springer, Berlin- Heidelberg-New York, 1972. · Zbl 0246.53031 [13] Kosniowski, C., Applications of holomorphic Lefschetz formula, Bull. London Math. Soc., 2 (1970), 43-48. · Zbl 0193.23903 [14] de Rham, G., Sur la division de formes et de courants par une forme lineaire, Comment. Math. Helv., 28 (1954), 346-352. · Zbl 0056.31601 [15] Sommese, A. J., Extension theorems for reductive group actions on compact Kahler manifolds, Math. Ann. 218 (1975), 107-116. · Zbl 0299.32029 [16] Sumihiro, H., Equivariant completion, Journal of Math. Kyoto Univ. 14 (1974), 1-28. Note added in proof. After submitting the paper the author was informed that the same resluts had also been obtained by J. B. Carrell and A. J. Sommese independently in the following two articles. [17] Carrell, J. B. and Sommese, J. B. C* actions, Math. Scand. 43 (1978), 49-60. [18] Carrell, J. B. and Sommese, J. B., Some topological aspects of C* actions on compact Kahler manifolds, preprint. · Zbl 0466.32015
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