Abstract
Let g ≥ 2 g \geq 2 and let the Torelli map denote the map sending a genus g g curve to its principally polarized Jacobian. We show that the restriction of the Torelli map to the hyperelliptic locus is an immersion in characteristic not 2 2 . In characteristic 2 2 , we show the Torelli map restricted to the hyperelliptic locus fails to be an immersion because it is generically inseparable; moreover, the induced map on tangent spaces has kernel of dimension g − 2 g-2 at every point.
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More From: Transactions of the American Mathematical Society, Series B
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