Abelian varieties and Riemann surfaces with generalized quaternion group action

نویسندگان

چکیده

We consider abelian varieties with a group of automorphisms isomorphic to generalized quaternion group. provide isogeny decompositions, compute dimensions the corresponding factors and give conditions under which this decomposition is nontrivial. then specialize our results Jacobians relate them so-called genus-zero actions on Riemann surfaces. A complete classification uniparametric families surfaces action given, extending known for quasiplatonic case. Finally, we construct explicit derive period matrix Jacobian surface full automorphism second largest order among hyperelliptic genus four.

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ژورنال

عنوان ژورنال: Journal of Pure and Applied Algebra

سال: 2023

ISSN: ['1873-1376', '0022-4049']

DOI: https://doi.org/10.1016/j.jpaa.2023.107398