On Prym varieties for the coverings of some singular plane curves

Lubjana Beshaj, Takuya Yamauchi

研究成果: ジャーナルへの寄稿学術論文査読

抄録

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).

本文言語英語
ページ(範囲)205-222
ページ数18
ジャーナルManuscripta Mathematica
158
1-2
DOI
出版ステータス出版済み - 2019 1月 7

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