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Homotopy groups of pullbacks of varieties

Published online by Cambridge University Press:  22 January 2016

Andrew John Sommese
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, U.S.A.
A. van de Ven
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, U.S.A.
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In [2, § 9] there is a general result of Fulton and Lazarsfeld relating the homotopy groups of a subvariety of in a certain range of dimensions with those of its pullback under a holomorphic map in the corresponding range of dimensions. It is asked in [2, § 10] whether here is a corresponding result with replaced by a general rational homogeneous manifold, Y, and with the range of dimensions alluded to above shifted by the ampleness of the holomorphic tangent bundle of Y in the sense of [4]. In this paper we use the techniques of [4, 5, 6, 7] to answer this question in the affirmative.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1986

References

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