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arXiv · 2201.11535

Degree-2 Abel maps and hyperelleptic curves

Alex Abreu·Sally Andria·Marco Pacini
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Abstract

In this paper we resolve the degree-2 Abel map for nodal curves. Our results are based on a previous work of the authors reducing the problem of the resolution of the Abel map to a combinatorial problem via tropical geometry. As an application, we characterize when the (symmetrized) degree-2 Abel map is not injective, a property that, for a smooth curve, is equivalent to the curve being hyperelliptic.

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Alex Abreu, Sally Andria, Marco Pacini. 2022-01-27. Degree-2 Abel maps and hyperelleptic curves. https://arxiv.org/abs/2201.11535

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