Geometry of quintics in $\mathbb P^3$ and the Craighero-Gattazzo surface of general type

Abstract

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.