It is an abelian variety$Z$ equipped with principal polarization$\Xi$ such that there exists an algebraic curve$C$ and an embedding $\iota \colon Z \hookrightarrow Jac(C)$ of $Z$ into its Jacobian variety such that the pullback of the principal polarization $\Theta$ of $Jac(C)$ along this embedding is an integral fraction of $\Xi$:

$\iota^\ast \Theta = n \Xi
\,.$

Here $n$ is called the exponent of $Z$ in $Jac(C)$.