Journal of Geometric Analysis

, Volume 21, Issue 3, pp 599–619 | Cite as

Hermitian Symmetric Polynomials and CR Complexity

Article

Abstract

Properties of Hermitian forms are used to investigate several natural questions from CR geometry. To each Hermitian symmetric polynomial we assign a Hermitian form. We study how the signature pairs of two Hermitian forms behave under the polynomial product. We show, except for three trivial cases, that every signature pair can be obtained from the product of two indefinite forms. We provide several new applications to the complexity theory of rational mappings between hyperquadrics, including a stability result about the existence of non-trivial rational mappings from a sphere to a hyperquadric with a given signature pair.

Keywords

Hermitian forms Embeddings of CR manifolds Hyperquadrics Signature pairs CR complexity theory Proper holomorphic mappings 

Mathematics Subject Classification (2000)

15B57 32V30 32H35 14P05 

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Copyright information

© Mathematica Josephina, Inc. 2010

Authors and Affiliations

  1. 1.Dept. of MathematicsUniv. of IllinoisUrbanaUSA

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