English

Towards the generalized Shapiro and Shapiro conjecture

Algebraic Geometry 2012-05-01 v1

Abstract

We find a new, asymptotically better, bound g14d2+O(d)g\le\frac14d^2+O(d) on the genus of a curve that may violate the generalized total reality conjecture. The bound covers all known cases except g=0g=0 (the original conjecture).

Keywords

Cite

@article{arxiv.0807.2044,
  title  = {Towards the generalized Shapiro and Shapiro conjecture},
  author = {Alex Degtyarev},
  journal= {arXiv preprint arXiv:0807.2044},
  year   = {2012}
}
R2 v1 2026-06-21T11:00:01.444Z