On the bad points of positive semidefinite polynomials
Algebraic Geometry
2022-05-24 v2
Abstract
A bad point of a positive semidefinite real polynomial f is a point at which a pole appears in all expressions of f as a sum of squares of rational functions. We show that quartic polynomials in three variables never have bad points. We give examples of positive semidefinite polynomials with a bad point at the origin, that are nevertheless sums of squares of formal power series, answering a question of Brumfiel. We also give an example of a positive semidefinite polynomial in three variables with a complex bad point that is not real, answering a question of Scheiderer.
Keywords
Cite
@article{arxiv.2103.16134,
title = {On the bad points of positive semidefinite polynomials},
author = {Olivier Benoist},
journal= {arXiv preprint arXiv:2103.16134},
year = {2022}
}
Comments
21 pages, final version