On intermediate Jacobians of cubic threefolds admitting an automorphism of order five

Bert van Geemen, Takuya Yamauchi

研究成果: Article査読

1 被引用数 (Scopus)

抄録

Let k be a field of characteristic zero containing a primitive fifth root of unity. Let X/k be a smooth cubic threefold with an automorphism of order five, then we observe that over a finite extension of the field actually the dihedral group D5 is a subgroup of Aut(X). We find that the intermediate Jacobian J(X) of X is isogenous to the product of an elliptic curve E and the self-product of an abelian surface B with real multiplication by Q(√5). We give explicit models of some algebraic curves related to the construction of J(X) as a Prym variety. This includes a two parameter family of curves of genus 2 whose Jacobians are isogenous to the abelian surfaces mentioned as above.

本文言語English
ページ(範囲)141-164
ページ数24
ジャーナルPure and Applied Mathematics Quarterly
12
1
DOI
出版ステータスPublished - 2016

ASJC Scopus subject areas

  • 数学 (全般)

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