### Abstract

Let k be a field of characteristic zero containing a primitive nth root of unity. Let Cn0 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 Prym(C~n/Cn) associated to the double cover 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 Prym(C~n/Cn) 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 Q(ζn+ζn-1).

Original language | English |
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Pages (from-to) | 205-222 |

Number of pages | 18 |

Journal | manuscripta mathematica |

Volume | 158 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 2019 Jan 7 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

*manuscripta mathematica*,

*158*(1-2), 205-222. https://doi.org/10.1007/s00229-018-1018-z