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 of any odd degree. We also construct a separating non-singular pseudoholomorphic curve in 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