Singularities of the theta divisor of the intermediate Jacobian of a double cover of $P^3$ of index two

In this paper a theorem is proved on the singularities of the Poincaré theta divisor $\Theta$ of the intermediate Jacobian of a body $X$, a double cover of $P^3$ of index two: the codimension of $\Theta$ in $J_3(X)$ is two. Hence a) $X$ is not rational, b) $(J_3(X),\Theta)$ is not a Prym variety, and, as a consequence, c) $X$ has no structure of a bundle of conics.
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