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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
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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Article copyright: © Copyright 1995 American Mathematical Society

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