Symmetric plane curves of degree 7 : pseudo-holomorphic and algebraic classifications

Details Symmetric plane curves of degree 7 : pseudo-holomorphic and algebraic classifications Symmetric plane curves of degree 7 : pseudo-holomorphic and algebraic classifications

2004-04-02

arxiv.org/abs/math/0404030v3

Mathematics

Geometric Topology

39 pages, 36 figures

Scientific paper

This paper is motivated by the real symplectic isotopy problem : does there exists a nonsingular real pseudoholomorphic curve not isotopic in the projective plane to any real algebraic curve of the same degree? Here, we focus our study on symmetric real curves on the projective plane. We give a classification of real schemes (resp. complex schemes) realizable by symmetric real curves of degree 7 with respect to the type of the curve (resp. M-symmetric real curves of degree 7). In particular, we exhibit two real schemes which are realizable by real symmetric dividing pseudoholomorphic curves of degree 7 on the projective plane but not by algebraic ones.

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