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arXiv · 2010.09130

Algebraically unrealizable complex orientations of plane real pseudoholomorphic curves

S. Yu. Orevkov
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Abstract

We prove two inequalities for the complex orientations of a separating (Type I) non-singular real algebraic curve in $RP^2$ of any odd degree. We also construct a separating non-singular pseudoholomorphic curve in $RP^2$ 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.

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S. Yu. Orevkov. 2021-05-06. Algebraically unrealizable complex orientations of plane real pseudoholomorphic curves. https://doi.org/10.1007/s00039-021-00569-1

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