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Algebraically unrealizable complex orientations of plane real pseudoholomorphic curves

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arxiv 2010.09130 v3 pith:RRV7PAVV submitted 2020-10-18 math.AG math.SG

S. Yu. Orevkov This is my paper · ORCID
classification math.AGmath.SG
keywords realalgebraicallycomplexcurvecurvesdegreeinequalitiesnon-singular
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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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  1. On finiteness properties of separating semigroup of real curve

    math.AG 2025-11 conditional novelty 7.0 of 10

    For each genus g, the set of all separating semigroups of real curves of genus g is finite.

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