  Let X be a complex projective n-dimensional manifold of general type, whose
canonical system is composite with a pencil. If the Albanese map is generically
finite, but not surjective, or if the irregularity is strictly larger than n
and the image of X in its Albanese variety of Kodaira dimension one, then the
geometric genus of a general fibre of the canonical map is one and the latter
factors through the Albanese map. The last part of this result holds true for
any threefold with irregularity 5 or larger.
