English

Algebraically unrealizable complex orientations of plane real pseudoholomorphic curves

Algebraic Geometry 2024-12-03 v3 Symplectic Geometry

Abstract

We prove two inequalities for the complex orientations of a separating (Type I) non-singular real algebraic curve in RP2RP^2 of any odd degree. We also construct a separating non-singular pseudoholomorphic curve in RP2RP^2 of any degree congruent to 9 mod 12 which does not satisfies one of these inequalities. Therefore the oriented isotopy type of the real locus of each of these curves is algebraically unrealizable.

Keywords

Cite

@article{arxiv.2010.09130,
  title  = {Algebraically unrealizable complex orientations of plane real pseudoholomorphic curves},
  author = {S. Yu. Orevkov},
  journal= {arXiv preprint arXiv:2010.09130},
  year   = {2024}
}

Comments

13 pages, 10 figures; v2: Remarks 1.7--1.9 are added; v3: a proof of Proposition 6.1 is added

R2 v1 2026-06-23T19:26:09.827Z