Geometry of Hermitian Algebraic Functions. Quotients of Squared Norms
Complex Variables
2007-05-23 v2 Algebraic Geometry
Abstract
Hermitian algebraic functions were introduced by Catlin and D'Angelo under the name of "globalizable metrics". Catlin and D'Angelo proved that any Hermitian algebraic function without non-trivial zeros is a quotient of squared norms, thus giving an answer to a Hermitian analogue of Hilbert's 17th problem in the non-degenerate 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.
Keywords
Cite
@article{arxiv.math/0504229,
title = {Geometry of Hermitian Algebraic Functions. Quotients of Squared Norms},
author = {Dror Varolin},
journal= {arXiv preprint arXiv:math/0504229},
year = {2007}
}
Comments
Major revision. Some errors in the proof corrected, and other incorrect results removed, but the main result remains the same