Nonnegative polynomials from vector bundles on real curves
Algebraic Geometry
2014-02-26 v2
Abstract
We observe that the E-resultant of a very ample rank 2 vector bundle E on a real projective curve (with no real points) is nonnegative when restricted to the space of real sections. Moreover, we show that if E has a section vanishing at exactly two points and the degree d of E satisfies d(d-6)> 4g-5, then this polynomial cannot be written as a sum of squares.
Cite
@article{arxiv.1208.6456,
title = {Nonnegative polynomials from vector bundles on real curves},
author = {Roger Bielawski},
journal= {arXiv preprint arXiv:1208.6456},
year = {2014}
}
Comments
6 pages; minor changes in version 2; to appear in the Bulletin of the LMS