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On the CR Transversality of Holomorphic Maps into Hyperquadrics

Dedicated to Professor Yum-Tong Siu on the occasion of his 70th birthday

  • 2015
  • OriginalPaper
  • Chapter
Published in:
Authors
Xiaojun Huang
Yuan Zhang
Published in
Complex Geometry and Dynamics
Publisher
Springer International Publishing

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Abstract

Let M ℓ be a smooth Levi-nondegenerate hypersurface of signature ℓ in C n with n ≥ 3, and write H ℓ N for the standard hyperquadric of the same signature in C N with \(N - n <\frac{n-1} {2}\). Let F be a holomorphic map sending M ℓ into \(H_{\ell}^{N}\). Assume F does not send a neighborhood of M ℓ in C n into \(H_{\ell}^{N}\). We show that F is necessarily CR transversal to M ℓ at any point. Equivalently, we show that F is a local CR embedding from M ℓ into \(H_{\ell}^{N}\).

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Metadata
Title
On the CR Transversality of Holomorphic Maps into Hyperquadrics
Authors
Xiaojun Huang
Yuan Zhang
Copyright Year
2015
Book
Complex Geometry and Dynamics

Print ISBN: 978-3-319-20336-2

Electronic ISBN: 978-3-319-20337-9

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-20337-9_7

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