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 -