Let $X$, $Y$ be compact Riemann surfaces and $\Theta_{X}$, $\Theta_{Y}$ the theta divisors on $J(X)$, $J(Y)$ respectively. Where $J(X):=$ Jacobian of the Riemann surface $X$.
My question is what does it mean an analytic isomorphism $\varphi:J(X)\longrightarrow J(Y)$ such that $\varphi^*(\Theta_{Y})=\Theta_{X}?$
I understand that $\varphi:J(X)\longrightarrow J(Y)$ is analytic isomorphism, that is biholomorphic between $J(X)$ and $J(Y)$ as Riemann surface, but I do not understand how to define the pull-back $\varphi^*$ such that $\varphi^*(\Theta_{Y})=\Theta_{X}?$
Any help is welcome, including books references.