English

Decomposable abelian $G$-curves and special subvarieties

Algebraic Geometry 2025-04-01 v2

Abstract

We consider families of abelian Galois coverings of the line. When the Jacobian of the general element is totally decomposable, i.e., is isogenous to a product of elliptic curves, we prove that they yield special subvarieties of \Ag\A_g if and only if a numerical condition holds, which in the general case is only known to be sufficient.

Keywords

Cite

@article{arxiv.2305.19030,
  title  = {Decomposable abelian $G$-curves and special subvarieties},
  author = {Irene Spelta and Carolina Tamborini},
  journal= {arXiv preprint arXiv:2305.19030},
  year   = {2025}
}

Comments

Significantly rewritten. The main theorem and its proof have been fixed, and the exposition has been improved