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]).
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