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arXiv · 1907.11407

On the geometry of the second fundamental form of the Torelli map

Paola Frediani·Gian Pietro Pirola
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Abstract

In this paper we give a geometric interpretation of the second fundamental form of the period map of curves and we use it to improve the upper bounds on the dimension of a totally geodesic subvariety Y of A_g generically contained in the Torelli locus obtained in [3], [7]. We get dim Y < 2g if g is even, dim Y < 2g+1 if g is odd. We also study totally geodesic subvarieties Z of A_g generically contained in the hyperelliptic Torelli locus and we show that dim Z < g+2.

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Paola Frediani, Gian Pietro Pirola. 2019-07-26. On the geometry of the second fundamental form of the Torelli map. https://doi.org/10.1090/proc%2F15291

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