English

Real plane sextics without real points

Algebraic Geometry 2025-05-19 v1

Abstract

We prove that the equisingular deformation type of a simple real plane sextic curve with smooth real part is determined by its real homological type, \ie, the polarization, exceptional divisors, and real structure recorded in the homology of the covering K3K3-surface. As an illustration, we obtain an equisingular deformation classification of real plane sextics with empty real part (for completeness, we consider the few non-simple ones as well).

Keywords

Cite

@article{arxiv.2403.01252,
  title  = {Real plane sextics without real points},
  author = {Alex Degtyarev and Ilia Itenberg},
  journal= {arXiv preprint arXiv:2403.01252},
  year   = {2025}
}
R2 v1 2026-06-28T15:07:10.561Z