Corpus ID: 212737176

Decomposing Jacobians via Galois covers.

  title={Decomposing Jacobians via Galois covers.},
  author={Davide Maria Lombardo and Elisa Lorenzo Garc{\'i}a and Christophe Ritzenthaler and Jeroen Sijsling},
  journal={arXiv: Algebraic Geometry},
  • Davide Maria Lombardo, Elisa Lorenzo García, +1 author Jeroen Sijsling
  • Published 2020
  • Mathematics
  • arXiv: Algebraic Geometry
  • Let $\phi:\,X\rightarrow Y$ be a (possibly ramified) cover between two algebraic curves of positive genus. We develop tools that may identify the Prym variety of $\phi$, up to isogeny, as the Jacobian of a quotient curve $C$ in the Galois closure of the composition of $\phi$ with a well-chosen map $Y\rightarrow \mathbb{P}^1$. This method allows us to recover all previously obtained descriptions of a Prym variety in terms of a Jacobian that are known to us, besides yielding new applications. We… CONTINUE READING