Symplectic W_8 and W_9 singularities

Żaneta Trębska

Journal of Singularities
volume 6 (2012), 158-178
Proceedings of the Workshop on Singularities in Geometry and Applications, Będlewo, 5 – 21 May 2011

Received: 31 December 2012. Received in revised form: 18 April 2012.

DOI: 10.5427/jsing.2012.6m

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In this paper we examine the singularities which are in the list of the simple 1-dimensional isolated complete intersection singularities in the space of dimension greater than 2, obtained by Giusti. Isolated complete intersection singularities (ICIS) were intensively studied by many authors, because of their interesting geometric, topological and algebraic properties. Here using the method of algebraic restrictions we obtain the complete symplectic classification of the singularities of type W_8 and W_9. We calculate discrete symplectic invariants for symplectic orbits of the curves and we give their geometric description. It allows us to explore the specific singular nature of these classical singularities that only appears in the presence of the symplectic structure.


symplectic manifold, curves, local symplectic algebra, algebraic restrictions, relative Darboux theorem, singularities

Mathematical Subject Classification:

Primary 53D05. Secondary 14H20, 58K50, 58A10

Author(s) information:

Żaneta Trębska
Warsaw University of Technology
Faculty of Mathematics and Information Science
Plac Politechniki 1
00-661 Warsaw, Poland