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Symmetric lagrangian singularities and Gauss maps of theta divisors

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1462)

Abstract

Recently three of the authors studied the Thom-Boardman singularities and the local ℤ/2-stability of the Gauss map of the theta divisor of a smooth algebraic curve of genus three [12]. In this paper we develop a theory of ℤ/2-symmetric Lagrangian maps appropriate to the study of theta divisors of curves of arbitrary genus, and we apply this theory to the genus three case, obtaining Lagrangian analogues of the results of [12]. We find that the local classification of ℤ/2-Lagrangian-stable Gauss maps coincides with our previous local classification of ℤ/2-stable Gauss maps in genus three. The corresponding classifications in higher genus are expected to diverge, as in the nonsymmetric case (cf.[3]).

Keywords

  • Isomorphism Class
  • Contact Structure
  • Orbit Space
  • Weierstrass Point
  • Hamiltonian Vector Field

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1991 Springer-Verlag Berlin Heidelberg

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Adams, M.R., McCrory, C., Shifrin, T., Varley, R. (1991). Symmetric lagrangian singularities and Gauss maps of theta divisors. In: Mond, D., Montaldi, J. (eds) Singularity Theory and its Applications. Lecture Notes in Mathematics, vol 1462. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086371

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  • DOI: https://doi.org/10.1007/BFb0086371

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53737-3

  • Online ISBN: 978-3-540-47060-1

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