Effective Iitaka fibrations

Abstract

We show that the M-canonical map of an n-dimensional complex projective manifold X of Kodaira dimension two is birational to an Iitaka fibration for a computable positive integer M. M depends on the index b of a general fibre F of the Iitaka fibration and on the Betti number of the canonical covering of F, In particular, M is a universal constant if the dimension n is smaller than or equal to 4.

19 pages, AMSLaTeX. Following suggestions of a referee, we added several comments and tried to improve the presentation of the results

References in corpus (4)

• Existence of minimal models for varieties of log general type
• Explicit birational geometry of threefolds of general type
• On a conjecture of Hacon and McKernan in dimension three
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Cited by in corpus (6)

• Non-algebraic Hyperkaehler manifolds
• Finite generation of a canonical ring
• On Effective log Iitaka Fibration for 3-folds and 4-folds
• On pluricanonical systems of algebraic varieties of general type
• Effective log Iitaka fibrations for surfaces and threefolds
• Relative Kähler-Einstein metric on Kähler varieties of positive Kodaira dimension