Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Effective Iitaka fibrations


Authors: Eckart Viehweg and De-Qi Zhang
Journal: J. Algebraic Geom. 18 (2009), 711-730
DOI: https://doi.org/10.1090/S1056-3911-09-00515-3
Published electronically: March 23, 2009
MathSciNet review: 2524596
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Abstract | References | Additional Information

Abstract: For every $n$-dimensional projective manifold $X$ of Kodaira dimension $2$ we show that $\Phi _{|M K_X|}$ is birational to an Iitaka fibration for a computable positive integer $M = M(b, B_{n-2})$, where $b > 0$ is minimal with $|bK_F| \ne \emptyset$ for a general fibre $F$ of an Iitaka fibration of $X$, and where $B_{n-2}$ is the Betti number of a smooth model of the canonical $\mathbb {Z}/(b)$-cover of the $(n-2)$-fold $F$. In particular, $M$ 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
MR Author ID: 187025
ORCID: 0000-0003-0139-645X
Email: matzdq@nus.edu.sg

Received by editor(s): June 14, 2007
Received by editor(s) in revised form: February 23, 2008
Published electronically: 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