The Torelli map restricted to the hyperelliptic locus

2019/11/05 by Landesman, Aaron
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1911.02084

Abstract

Let g ≥ 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.

Related

• The infinitesimal Torelli problem
• On some differential-geometric aspects of the Torelli map
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• Hyperelliptic Jacobians and isogenies
• Higher Gaussian maps on the hyperelliptic locus and second fundamental form