Local symplectic algebra of quasi-homogeneous curves

Details Local symplectic algebra of quasi-homogeneous curves Local symplectic algebra of quasi-homogeneous curves

2008-05-29

arxiv.org/abs/0805.4569v2

Fundamenta Mathematicae 204(2009), 57-86

Mathematics

Symplectic Geometry

25 pages, a new version

Scientific paper

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).

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