Hermitian complexity of real polynomial ideals

John P. D'Angelo, Mihai Putinar

Research output: Contribution to journalArticlepeer-review


We define the Hermitian complexity of a real polynomial ideal and of a real algebraic subset of C n. This concept is aimed at determining precise necessary conditions for a Hermitian symmetric polynomial to agree with a Hermitian squared norm on an algebraic set. The latter topic has been a central theme in modern polynomial optimization and in complex geometry, specifically related to the holomorphic embedding of pseudoconvex domain into balls, or the classification of proper holomorphic maps between balls.

Original languageEnglish (US)
Article number1250026
JournalInternational Journal of Mathematics
Issue number6
StatePublished - Jun 2012


  • CR complexity
  • Hermitian forms
  • Hermitian length
  • Hilbert's 17th problem
  • algebraic sets
  • positivity conditions
  • sums of squares

ASJC Scopus subject areas

  • Mathematics(all)

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