Classification of simple multigerms of curves in a space with symplectic structure
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P. A. Kolgushkin
Translated by: N. Yu. Netsvetaev - St. Petersburg Math. J. 15 (2004), 103-126
- DOI: https://doi.org/10.1090/S1061-0022-03-00804-5
- Published electronically: December 31, 2003
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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.References
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Bibliographic Information
- P. A. Kolgushkin
- Affiliation: Moscow State University, Mechanics and Mathematics Department, Moscow 119899, Russia
- Email: kolgush@mccme.ru
- 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).
- © Copyright 2003 American Mathematical Society
- Journal: St. Petersburg Math. J. 15 (2004), 103-126
- MSC (2000): Primary 57R45
- DOI: https://doi.org/10.1090/S1061-0022-03-00804-5
- MathSciNet review: 1979720