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arXiv · 2509.00998

The Torelli locus and Newton polygons

Rachel Pries
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Abstract

This manuscript is about abelian varieties that are Jacobians of curves. I started writing it for a lecture series at the Arizona Winter School in 2024 on abelian varieties. A longer more descriptive title might be: The Torelli locus in the moduli space of abelian varieties, with applications to Newton polygons of curves in positive characteristic. To elaborate, this manuscript covers two topics: the first is about the geometry of the Torelli locus; the second is about the arithmetic invariants of abelian varieties that occur for Jacobians of smooth curves in positive characteristic.

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Rachel Pries. 2025-08-31. The Torelli locus and Newton polygons. https://arxiv.org/abs/2509.00998

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