Geometry of Hermitian algebraic functions. Quotients of squared norms

• Autores: Dror Varolin
• Localización: American journal of mathematics, ISSN 0002-9327, Vol. 130, Nº 2, 2008, págs. 291-315
• Idioma: inglés
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• Resumen

  • Hermitian algebraic functions were introduced by D. Catlin and J. D'Angelo under the name of "globalizable metrics". Catlin and D'Angelo proved that any Hermitian algebraic function without nontrivial zeros is a quotient of squared norms, thus giving an answer to a Hermitian analogue of Hilbert's 17th problem in the nondegenerate case. The result was independently proved somewhat earlier by D. Quillen in a special case, and using different methods. In this paper, we characterize all Hermitian algebraic functions that are quotients of squared norms.