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Degree-2 Abel maps and hyperelleptic curves

2022/01/27 by Alex Abreu, Abreu, Alex, Sally Andria +3
Computer Science · Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Nonlinear Waves and Solitons #Polynomial and algebraic computation #math.AG #msc:14H10 #msc:14H40 #msc:14T90

paper · pdf · doi:10.48550/arxiv.2201.11535

19 pages, 10 figures

arxiv created 2022/01/27 · arxiv updated 2022/01/28

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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