A note on Jacobians of quasiplatonic Riemann surfaces with complex multiplication

Abstract

Let $m⩾6$ be an even integer. In this short note we prove that the Jacobian variety of a quasiplatonic Riemann surface with associated group of automorphisms isomorphic to $C_2^2{⋊}_2{C}_m$ admits complex multiplication. We then extend this result to provide a criterion under which the Jacobian variety of a quasiplatonic Riemann surface admits complex multiplication.

6 pages, A typo is corrected. To appear in Geometriae Dedicata

References in corpus (1)

• Quasiplatonic curves with symmetry group ${\mathbb{Z}}_2^2⋊{\mathbb{Z}}_m$ are definable over $\mathbb{Q}$