  In this paper we study the question whether the tri-canonical system on the
Craighero-Gattazzo surface is base point free and at which points does it
separate tangent vectors. Also we study the non-rationality of the
normalization of the quotient of a general curve (under a given involution) in
the product linear system of cubics and quadrics on a singular quintic in
$\PR^3$ with four elliptic singularities.
