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Irregular manifolds with a canonical linear system, composite with a pencil

Jin-Xing Cai·Eckart Viehweg
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Abstract

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.

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Jin-Xing Cai, Eckart Viehweg. 2003-03-17. Irregular manifolds with a canonical linear system, composite with a pencil. https://arxiv.org/abs/math/0303196

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