TY - JOUR
T1 - On Holomorphic Curves Tangent to Real Hypersurfaces of Infinite Type
AU - Kamimoto, Joe
N1 - Funding Information:
The author greatly appreciates that Ninh Van Thu kindly informed of important examples of real hypersurfaces of infinite type in []. The author also would like to express his sincere gratitude to the referee for his/her careful reading of the manuscript and giving the author valuable comments. This work was supported by JSPS KAKENHI Grant Numbers JP20K03656, JP20H00116.
Publisher Copyright:
© 2020, The Author(s).
PY - 2021/8
Y1 - 2021/8
N2 - The purpose of this paper is to investigate the geometric properties of real hypersurfaces of D’Angelo infinite type in Cn. 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.
AB - The purpose of this paper is to investigate the geometric properties of real hypersurfaces of D’Angelo infinite type in Cn. 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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U2 - 10.1007/s12220-020-00567-z
DO - 10.1007/s12220-020-00567-z
M3 - Article
AN - SCOPUS:85097192591
SN - 1050-6926
VL - 31
SP - 8063
EP - 8079
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 8
ER -