Decomposing Jacobians via Galois covers
Abstract
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 wellchosen 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 also find algebraic equations for some of these new cases, including one where $X$ has genus $3$, $Y$ has genus $1$ and $\phi$ is a degree $3$ map totally ramified over $2$ points.
 Publication:

arXiv eprints
 Pub Date:
 March 2020
 arXiv:
 arXiv:2003.07774
 Bibcode:
 2020arXiv200307774L
 Keywords:

 Mathematics  Algebraic Geometry;
 14K20;
 14K25;
 14J15;
 11F46;
 14L24