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arXiv · 1911.02084

The Torelli map restricted to the hyperelliptic locus

Aaron Landesman
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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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Aaron Landesman. 2019-11-05. The Torelli map restricted to the hyperelliptic locus. https://arxiv.org/abs/1911.02084

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