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 $n \le 4$.
References
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References
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- E. Viehweg, Weak positivity and the additivity of the Kodaira dimension for certain fibre spaces. Algebraic varieties and analytic varieties (Tokyo, 1981) 329–353, Adv. Stud. Pure Math., 1, North-Holland, Amsterdam, 1983. MR 715656 (85b:14041)
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- D. -Q. Zhang, Logarithmic del Pezzo surfaces of rank one with contractible boundaries. Osaka J. Math. 25 (1988) 461–497. MR 957874 (89k:14059)
Additional Information
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
