Irregular canonical double surfaces

Abstract

We study minimal surfaces X of general type with $K_X^2=6p_g-14$ and $q(X)>0$ such that $K_X$ is ample, the image of the canonical map is a canonically embedded surface of general type and the canonical map is not birational. The main result states that if X satisfies the above assumptions and $q(X)\ge 2$, then, apart from a finite number of exceptions, X belongs to an infinite series of examples due to Beauville. The exceptions are described in detail and some new examples are given.

LaTeX 2.09, 22 pages, the proof of the main result has been simplified