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Classification of simple multigerms of curves in a space with symplectic structure


Author: P. A. Kolgushkin
Translated by: N. Yu. Netsvetaev
Original publication: Algebra i Analiz, tom 15 (2003), nomer 1.
Journal: St. Petersburg Math. J. 15 (2004), 103-126
MSC (2000): Primary 57R45
DOI: https://doi.org/10.1090/S1061-0022-03-00804-5
Published electronically: December 31, 2003
MathSciNet review: 1979720
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Abstract | References | Similar Articles | Additional Information

Abstract: A classification of stably simple germs of curves (both reducible and irreducible) in the complex space equipped with a symplectic structure is obtained. This classification extends the result by V. I. Arnol'd of 1999, which described the $A_{2k}$ singularities in the symplectic complex space. The proofs involve the homotopy method and the Darboux-Givental theorem.


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Additional Information

P. A. Kolgushkin
Affiliation: Moscow State University, Mechanics and Mathematics Department, Moscow 119899, Russia
Email: kolgush@mccme.ru

DOI: https://doi.org/10.1090/S1061-0022-03-00804-5
Keywords: Symplectomorphism, stably simple singularity, multigerm
Received by editor(s): January 29, 2002
Published electronically: December 31, 2003
Additional Notes: Partly supported by RFBR (grant no. 01-01-00739) and by NWD-RFBR (grant no. 047.008.005).
Article copyright: © Copyright 2003 American Mathematical Society

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