Indices of holomorphic vector fields relative to invariant curves on surfaces

Suwa, Tatsuo

doi:10.1090/S0002-9939-1995-1291793-0

Indices of holomorphic vector fields relative to invariant curves on surfaces
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Proc. Amer. Math. Soc. 123 (1995), 2989-2997 Request permission

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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