Local symplectic algebra of quasi-homogeneous curves

被引:8
|
作者
Domitrz, Wojciech [1 ,2 ]
机构
[1] Warsaw Univ Technol, Fac Math & Informat Sci, PL-00661 Warsaw, Poland
[2] Polish Acad Sci, Inst Math, PL-00956 Warsaw, Poland
关键词
symplectic manifold; curves; local symplectic algebra; algebraic restrictions; relative Darboux theorem; singularities; SIMPLE SINGULARITIES;
D O I
10.4064/fm204-1-4
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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).
引用
收藏
页码:57 / 86
页数:30
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