Asian Journal of Mathematics

Volume 8 (2004)

Number 1

IRREGULAR MANIFOLDS WHOSE CANONICAL SYSTEM IS COMPOSED OF A PENCIL

Pages: 27 – 38

DOI: http://dx.doi.org/10.4310/AJM.2004.v8.n1.a4

Authors

JIN-XING CAI

ECKART VIEHWEG

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 Alb(X) is of Kodaira dimension one, then the geometric genus pg(F) of a general fibre F 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 q(X) ≥ 5.

Full Text (PDF format)