Resumen de Geometry of Hermitian algebraic functions. Quotients of squared norms

Dror Varolin

• 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.