Algebraically unrealizable complex orientations of plane real pseudoholomorphic curves

Abstract

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

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

References in corpus (2)

• The separating semigroup of a real curve
• Corrigendum to the paper "A flexible affine $M$-sextic which is algebraically unrealizable"