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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Hermitian vector bundles and value distribution for Schubert cycles


Author: Michael J. Cowen
Journal: Trans. Amer. Math. Soc. 180 (1973), 189-228
MSC: Primary 32H25
DOI: https://doi.org/10.1090/S0002-9947-1973-0333252-5
MathSciNet review: 0333252
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Abstract: R. Bott and S. S. Chern used the theory of characteristic differential forms of a holomorphic hermitian vector bundle to study the distribution of zeroes of a holomorphic section. In this paper their methods are extended to study how often a holomorphic mapping into a Grassmann manifold hits Schubert cycles of fixed type.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0333252-5
Keywords: First Main Theorem, Schubert cycle, Hermitian vector bundle, refined Chern class, Chern duality, ample vector bundle
Article copyright: © Copyright 1973 American Mathematical Society