Symplectic classification of parametric complex plane curves
Volume 99 / 2010
Annales Polonici Mathematici 99 (2010), 263-284
MSC: Primary 58K50; Secondary 14H20, 58D27.
DOI: 10.4064/ap99-3-4
Abstract
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.
