Local symplectic algebra of quasi-homogeneous curves

• Autorzy: Wojciech Domitrz
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 58K50: Normal forms
• 53D05: Symplectic manifolds, general
• 14H20: Singularities, local rings
• 58A10: Differential forms

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2009
• Tom: 204
• Numer: 1
• Strony: 57-86

Daty

wydano

2009

Twórcy

autor

Wojciech Domitrz

• Faculty of Mathematics and Information Science, Warsaw University of Technology, Plac Politechniki 1, 00-661 Warszawa, Poland
• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 21, 00-956 Warszawa, Poland

Identyfikatory

DOI

10.4064/fm204-1-4