2008/05/31 by Wojciech Domitrz · 1 citation
Mathematics · #math.SG #math.AG #msc:53D05 #msc:14H20 #msc:58K50 #msc:58A10
published as Fundamenta Mathematicae 204(2009), 57-86 · 25 pages, a new version
We study the local symplectic algebra of parameterized curves introduced by V. I. Arnold. We use the method of algebraic restrictions to classify symplectic singularities of quasi-homogeneous curves. We prove that the space of algebraic restrictions of closed 2-forms to the germ of an analytic curve is a finite dimensional vector space. We also show that the action of local diffeomorphisms preserving the curve on this vector space is determined by the infinitesimal action of liftable vector fields. We apply these results to obtain the complete symplectic classification of curves with the semigroups (3,4,5), (3,5,7), (3,7,8).