Symplectic classification of parametric complex plane curves

Volume 99 / 2010

Goo Ishikawa, Stanisław Janeczko Annales Polonici Mathematici 99 (2010), 263-284 MSC: Primary 58K50; Secondary 14H20, 58D27. DOI: 10.4064/ap99-3-4


Based on the discovery that the $\delta $-invariant is the symplectic codimension of a parametric plane curve singularity, we classify the simple and uni-modal singularities of parametric plane curves under symplectic equivalence. A new symplectic deformation theory of curve singularities is established, and the corresponding cyclic symplectic moduli spaces are reconstructed as canonical ambient spaces for the diffeomorphism moduli spaces which are no longer Hausdorff spaces.


  • Goo IshikawaDepartment of Mathematics
    Hokkaido University
    Sapporo 060-0810, Japan
  • Stanisław JaneczkoInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-956 Warszawa, Poland
    Faculty of Mathematics and Information Science
    Warsaw University of Technology
    Pl. Politechniki 1
    00-661 Warszawa, Poland

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