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 a 𝕂-analytic curve is a finite-dimensional vector space. We also show that the action of local diffeomorphisms preserving the quasi-homogeneous curve on this vector space is determined by the infinitesimal action of liftable vector fields. We apply these results to obtain a complete symplectic classification of curves with semigroups (3,4,5), (3,5,7), (3,7,8).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm204-1-4,
author = {Wojciech Domitrz},
title = {Local symplectic algebra of quasi-homogeneous curves},
journal = {Fundamenta Mathematicae},
volume = {205},
year = {2009},
pages = {57-86},
zbl = {1173.53038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm204-1-4}
}
Wojciech Domitrz. Local symplectic algebra of quasi-homogeneous curves. Fundamenta Mathematicae, Tome 205 (2009) pp. 57-86. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm204-1-4/