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Transactions of the American Mathematical Society

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

 

 

On the zero set of a holomorphic one-form on a compact complex manifold


Author: Michael J. Spurr
Journal: Trans. Amer. Math. Soc. 308 (1988), 329-339
MSC: Primary 32J15; Secondary 32L10, 32L99
DOI: https://doi.org/10.1090/S0002-9947-1988-0946446-3
MathSciNet review: 946446
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Abstract: On any compact complex surface $ M$, divisors of nonnegative self-intersection which are contained in the zero set (or in the integral set) of a holomorphic $ 1$-form are shown to induce a fibration of $ M$ onto a Riemann surface. This result is extended to higher dimensions for $ M$ projective. Applications to zero sets of holomorphic $ 1$-forms on surfaces are given.


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DOI: https://doi.org/10.1090/S0002-9947-1988-0946446-3
Article copyright: © Copyright 1988 American Mathematical Society