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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Indices of holomorphic vector fields relative to invariant curves on surfaces


Author: Tatsuo Suwa
Journal: Proc. Amer. Math. Soc. 123 (1995), 2989-2997
MSC: Primary 32S65; Secondary 32L30
DOI: https://doi.org/10.1090/S0002-9939-1995-1291793-0
MathSciNet review: 1291793
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Abstract: The local index of a holomorphic vector field relative to a (possibly singular) invariant complex analytic curve on a complex surface is defined and it is shown that, for a compact curve invariant by a one-dimensional singular foliation on a surface, the sum of the indices is equal to its self-intersection number. An interpretation of the indices in terms of holonomy is also given.


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DOI: https://doi.org/10.1090/S0002-9939-1995-1291793-0
Article copyright: © Copyright 1995 American Mathematical Society