The Gauss map of a genus three theta divisor

McCrory, Clint; Shifrin, Theodore; Varley, Robert

doi:10.1090/S0002-9947-1992-1070351-9

The Gauss map of a genus three theta divisor
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Trans. Amer. Math. Soc. 331 (1992), 727-750 Request permission

Abstract:

A smooth complex curve is determined by the Gauss map of the theta divisor of the Jacobian variety of the curve. The Gauss map is invariant with respect to the $(- 1)$-map of the Jacobian. We show that for a generic genus three curve the Gauss map is locally ${\mathbf {Z}}/2$-stable. One method of proof is to analyze the first-order ${\mathbf {Z}}/2$-deformations of the Gauss map of a hyperelliptic theta divisor.

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