Topologie Des ($M - 2$)-Courbes Réelles Symétriques

Trilles, Sébastien

doi:10.1112/s0024609302001698

Cited by 2 publications

(2 citation statements)

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“…Such a real plane curve, invariant under a symmetry, is called a symmetric curve. The systematic study of symmetric curves was started by T. Fiedler ( [Fie]) and continued by S. Trille ( [Tri01], [Tri03]). The rigid isotopy classes (two nonsingular curves of degree m on RP 2 are said to be rigidly isotopic if they belong to the same connected component of the complement of the discriminant hypersurface in the space of curves of degree m) of nonsingular sextics in RP 2 which contain a symmetric curve can be obtained from [Ite95].…”

Section: Brief Historymentioning

confidence: 99%

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Symmetric plane curves of degree 7: pseudoholomorphic and algebraic classifications

Brugallé

2007

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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This paper is motivated by the real symplectic isotopy problem : does there exist 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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Section: Brief Historymentioning

confidence: 99%

“…Proposition 2.15 (Trille, [Tri03]) If a symmetric curve on RP 2 and its mirror curve are of type I, so is the quotient curve.…”

Section: General Facts About Symmetric Curves On the Real Planementioning

confidence: 99%