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arXiv · 2011.05044

On holomorphic curves tangent to real hypersurfaces of infinite type

Joe Kamimoto
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Abstract

The purpose of this paper is to investigate the geometric properties of real hypersurfaces of D'Angelo infinite type in ${\mathbb C}^n$. In order to understand the situation of flatness of these hypersurfaces, it is natural to ask whether there exists a nonconstant holomorphic curve tangent to a given hypersurface to infinite order. A sufficient condition for this existence is given by using Newton polyhedra,which is an important concept in singularity theory. More precisely,equivalence conditions are given in the case of some model hypersurfaces.

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Joe Kamimoto. 2020-11-10. On holomorphic curves tangent to real hypersurfaces of infinite type. https://doi.org/10.1007/s12220-020-00567-z

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