Global classification of curves on the symplectic plane

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dc.creatorIshikawa, Goo
dc.date2007-02-21
dc.date.accessioned2026-07-07T07:48:01Z
dc.date.available2026-07-07T07:48:01Z
dc.descriptionWe consider the global symplectic classification problem of plane curves. First we give the exact classification result under symplectomorphisms, for the case of generic plane curves, namely immersions with transverse self-intersections. Then the set of symplectic classes form the symplectic moduli space which we completely describe by its global topological term. For the general plane curves with singularities, the difference between symplectomorphism and diffeomorphism classifications is clearly described by local symplectic moduli spaces of singularities and a global topological term. We introduce the symplectic moduli space of a global plane curve and the local symplectic moduli space of a plane curve singularity as quotients of mapping spaces, and we endow them with differentiable structures in a natural way.
dc.description25 pages 3 figures
dc.identifierhttps://arxiv.org/abs/math/0702602
dc.identifierhttp://arxiv.org/abs/math/0702602
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/124358
dc.subjectDifferential Geometry
dc.subjectSymplectic Geometry
dc.subject58K40; 58C27, 58D15, 53Dxx
dc.titleGlobal classification of curves on the symplectic plane
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