Hermitian symmetric polynomials and CR complexity

John P. D'Angelo, Jiří Lebl

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)599-619
Number of pages21
JournalJournal of Geometric Analysis
Volume21
Issue number3
DOIs
StatePublished - Jul 2011

Keywords

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

ASJC Scopus subject areas

  • Geometry and Topology

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