Jacobians with complex multiplication
By Á. Carocca, Herbert Lange, R. Rodríguez. 2009
58 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/1a3854e65b1f9c2ae231ceacddf8b44e767de805
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In Computational Theory and Mathematics
In Geometry and Topology
- B. Moonen
- Paola Porru
- P. Frediani
- Gerard van der Geer
- Frans Oort
- E. Colombo
- Matteo Penegini
- Raf Bocklandt
Citations in the corpus
- Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication (2007, unknown): “In [29] J.”
- On totally geodesic submanifolds in the Jacobian locus (2013, background): “[7, 21, 25], since they provide the only known examples of totally geodesic submanifolds contained in the Jacobian locus.”
- Good reduction of abelian varieties (2014, result): “This family has been studied, amongst others, by de Jong and Noot in [9].”
- Shimura varieties in the Torelli locus via Galois coverings of elliptic curves (2014, methodology): “In [13] the authors systematically studied families of Galois covering of P1 following the previous work done by Moonen [28] in the cyclic case and initiated in [38, 30, 10, 36] (see also the survey [29, §5]).”
- The Torelli locus and special subvarieties (2011, result): “As we shall discuss below, when combined with the results of Hain and de Jong-Zhang, these results can be used to obtain some restrictions on the special subvarieties of PEL type that are contained in the Torelli locus.”