The characterization of holomorphic vector fields vanishing at an infinite type point (Q655470)
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scientific article; zbMATH DE number 5994329
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The characterization of holomorphic vector fields vanishing at an infinite type point |
scientific article; zbMATH DE number 5994329 |
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The characterization of holomorphic vector fields vanishing at an infinite type point (English)
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4 January 2012
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Let \(M\) be the germ of a rotationally invariant smooth hypersurface in \(\mathbb C^2\) around the origin \(O\). It is assumed that \(O\) is a point of infinite type and that it is an isolated point of the intersection of \(M\) and its complex tangent. Then the only local infinitesimal automorphism of \(M\) that fixes the origin is the vector field generating the rotational symmetry. This can be considered as a confirmation of a conjecture by Greene and Krantz in a particular case.
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hypersurface
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infinite type
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infinitesimal automorphism
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Greene-Krantz conjecture
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