Group actions on Jacobian varieties

By Anita M. Rojas. 2003

56 citations recorded by the source corpus.

Consider a finite group $G$ acting on a Riemann surface $S$, and the associated branched Galois cover $\pi_G:S \to Y=S/G$. We introduce the concept of geometric signature for the action of $G$, and we show that it captures the information of the geometric structure of the lattice of intermediate covers, the information about the isotypical decomposition of the rational representation of the group $G$ acting on the Jacobian variety $JS$ of $S$, and the dimension of the subvarieties of the isogeny decomposition of $JS$. We also give a version of Riemann's existence theorem, adjusted to the present setting.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1a7c33462b4b9333b8f6833f63011040b435d6dc

How researchers see this paper

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In Geometry and Topology

1. Herbert Lange
2. Anita M. Rojas
3. P. Frediani

In Mathematical Physics

1. Herbert Lange
2. Anita M. Rojas

Citations in the corpus

• Jacobians with complex multiplication (2009, background): “This is a consequence of [7, Theorem 5.12], which in our case says where K χ 1 denotes the field generated by the values of the character χ 1 over Q , G 1 = (cid”