Global Prym-Torelli for double coverings ramified in at least 6 points

2020/05/22 by Juan Carlos Naranjo, Naranjo, Juan Carlos, Ángela Ortega +1 · 1 citation
Mathematics · Physics and Astronomy · #14H40 #14K10 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2005.11108

openalex publication_date 2020/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the ramified Prym map \mathcal P_{g, r} which sends a covering π:D\longrightarrow C ramified in r points to the Prym variety P(π):=Ker(Nm_π) is an embedding for all r≥ 6 and for all g(C)>0. Moreover, by studying the restriction to the locus of coverings of hyperelliptic curves, we show that \mathcal P_{g, 2} and \mathcal P_{g, 4} have positive dimensional fibers.

Citations

• On the projective normality of complete linear series on an algebraic curve

Cited by

• Explicit analysis of positive dimensional fibres of P_g,r and Xiao conjecture

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