Let $X\rightarrow Y$ a ramifield double cover of curves, $J_X, J_Y$ their jacobians, $P\subset J_X$ the Prym variety, for any line bundle $L$ on $X$ of degree $g_X-1$, denote by $\Theta_L$ the pullback of Riemann theta divisor $\Theta\subset Pic^{g_X-1}(X)$ by the translation map,
For which $L\in Pic^{g_X-1}(X)$, we have $P\not\subset \Theta_L$? and does the restriction of this divisor to $P$ gives a divisor? Any reference will be appreciated.
Many thanks
