English

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.

Keywords

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

R2 v1 2026-06-21T21:57:55.052Z