2007/02/21 by Goo Ishikawa, Ishikawa, Goo
Mathematics · #53Dxx #58C27 #58D15 #58K40 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG) #math.DG #math.SG #msc:53Dxx #msc:58C27 #msc:58D15 #msc:58K40
paper · pdf · doi:10.48550/arxiv.math/0702602
25 pages 3 figures
arxiv created 2007/02/21 · openalex publication_date 2007/02/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We 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.