Mathematical Research Letters
Volume 17 (2010)
Sums of hermitian squares on pseudoconvex boundaries
Pages: 1047 – 1053
We give an abstract characterization of all real algebraic subvarieties of complex affine space on which every positive polynomial is a sum of hermitian squares, and we find obstructions to this phenomenon. As a consequence we construct a strictly pseudoconvex domain with smooth algebraic boundary on which there exists a degree two positive polynomial which is not a sum of hermitian squares, answering thus in the negative a question of John D'Angelo.