Journal of Algebraic Geometry

Author(s): Eckart Viehweg; De-Qi Zhang
Journal: J. Algebraic Geom. 18 (2009), 711-730.
Posted: March 23, 2009
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Abstract: For every

-dimensional projective manifold

of Kodaira dimension

we show that $\Phi_{\vert M K_X\vert}$ is birational to an Iitaka fibration for a computable positive integer $M = M(b, B_{n-2})$ , where

is minimal with $\vert bK_F\vert \ne \emptyset$ for a general fibre

of an Iitaka fibration of

, and where $B_{n-2}$ is the Betti number of a smooth model of the canonical $\mathbb{Z}/(b)$ -cover of the

-fold

. In particular,

is a universal constant if the dimension $n \le 4$ .

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Eckart Viehweg
Affiliation: Universität Duisburg-Essen, Fachbereich Mathematik, 45117 Essen, Germany
Email: viehweg@uni-due.de

De-Qi Zhang
Affiliation: Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Singapore
Email: matzdq@nus.edu.sg

PII: S 1056-3911(09)00515-3
Received by editor(s): June 14, 2007
Received by editor(s) in revised form: February 23, 2008
Posted: March 23, 2009
Additional Notes: This work has been supported by the DFG-Leibniz program and by the SFB/TR 45 ``Periods, moduli spaces and arithmetic of algebraic varieties''. The second author is partially supported by an academic research fund of NUS

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