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manuscripta mathematica

, Volume 158, Issue 1–2, pp 205–222 | Cite as

On Prym varieties for the coverings of some singular plane curves

  • Lubjana Beshaj
  • Takuya YamauchiEmail author
Article
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Abstract

Let k be a field of characteristic zero containing a primitive nth root of unity. Let \(C^0_n\) be a singular plane curve of degree n over k admitting an order n automorphism, n nodes as the singularities, and \(C_n\) be its normalization. In this paper we study the factors of Prym variety \(\text{ Prym }(\widetilde{C}_n/C_n)\) associated to the double cover \(\widetilde{C}_n\) of \(C_n\) exactly ramified at the points obtained by the blow-up of the singularities. We provide explicit models of some algebraic curves related to the construction of \(\text{ Prym }(\widetilde{C}_n/C_n)\) as a Prym variety and determine the interesting simple factors other than elliptic curves or hyperelliptic curves with small genus which come up in \(J_n\) so that the endomorphism rings contains the totally real field \(\mathbb {Q}(\zeta _n+\zeta ^{-1}_n)\).

Mathematics Subject Classification

14H40 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Army Cyber InstituteUnited States Military AcademyWest PointUSA
  2. 2.Mathematics InstituteTohoku UniversitySendaiJapan

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