Vol. 108, No. 2, 1983

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ISSN: 0030-8730
On the vector fields on an algebraic homogeneous space

Yoshifumi Kato

Vol. 108 (1983), No. 2, 285–294
Abstract

We construct a holomorphic vector field V with isolated zeros on an algebraic homogeneous space X = G∕P and show that the Koszul complex defined by V gives much information concerning the cohomology groups of X. Our results give useful examples to the studies of J. B. Carrell and D. Lieberman.

Mathematical Subject Classification 2000
Primary: 32M10
Secondary: 14M17, 32L99
Milestones
Received: 6 November 1980
Revised: 1 July 1981
Published: 1 October 1983
Authors
Yoshifumi Kato