Geometry of Hermitian Algebraic Functions. Quotients of Squared Norms

الأصل · EN

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.