Mathematics – Geometric Topology
Scientific paper
2004-04-02
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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