TY - JOUR

T1 - On Prym varieties for the coverings of some singular plane curves

AU - Beshaj, Lubjana

AU - Yamauchi, Takuya

N1 - Funding Information:
Takuya Yamauchi is partially supported by JSPS Grant-in-Aid for Scientific Research (C) No. 15K04787.
Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2019/1/7

Y1 - 2019/1/7

N2 - 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 Cn 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 Cn 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 Jn so that the endomorphism rings contains the totally real field Q(ζn+ζn-1).

AB - 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 Cn 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 Cn 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 Jn so that the endomorphism rings contains the totally real field Q(ζn+ζn-1).

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U2 - 10.1007/s00229-018-1018-z

DO - 10.1007/s00229-018-1018-z

M3 - Article

AN - SCOPUS:85043357995

VL - 158

SP - 205

EP - 222

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

SN - 0025-2611

IS - 1-2

ER -