The Torelli map restricted to the hyperelliptic locus

Landesman, Aaron

doi:10.1090/btran/64

The Torelli map restricted to the hyperelliptic locus
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Trans. Amer. Math. Soc. Ser. B 8 (2021), 354-378

Abstract:

Let $g \geq 2$ and let the Torelli map denote the map sending a genus $g$ 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 $2$. In characteristic $2$, 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 $g-2$ at every point.

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