Local symplectic algebra of quasi-homogeneous curves

Wojciech Domitrz. "Local symplectic algebra of quasi-homogeneous curves." Fundamenta Mathematicae 204.1 (2009): 57-86. <http://eudml.org/doc/282841>.

@article{WojciechDomitrz2009,
abstract = {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).},
author = {Wojciech Domitrz},
journal = {Fundamenta Mathematicae},
keywords = {symplectic manifold; curves; local symplectic algebra; algebraic restrictions; relative Darboux theorem; singularities},
language = {eng},
number = {1},
pages = {57-86},
title = {Local symplectic algebra of quasi-homogeneous curves},
url = {http://eudml.org/doc/282841},
volume = {204},
year = {2009},
}

TY - JOUR
AU - Wojciech Domitrz
TI - Local symplectic algebra of quasi-homogeneous curves
JO - Fundamenta Mathematicae
PY - 2009
VL - 204
IS - 1
SP - 57
EP - 86
AB - 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).
LA - eng
KW - symplectic manifold; curves; local symplectic algebra; algebraic restrictions; relative Darboux theorem; singularities
UR - http://eudml.org/doc/282841
ER -