Jacobians with complex multiplication

Abstract:

We construct and study two series of curves whose Jacobians admit complex multiplication. The curves arise as quotients of Galois coverings of the projective line with Galois group metacyclic groups $G_{q,3}$ of order $3q$ with $q \equiv 1 \mod 3$ an odd prime, and $G_m$ of order $2^{m+1}$. The complex multiplications arise as quotients of double coset algebras of the Galois groups of these coverings. We work out the CM-types and show that the Jacobians are simple abelian varieties.