Pluricanonical maps of varieties of maximal Albanese dimension
Journal
Mathematische Annalen
Journal Volume
320
Journal Issue
2
Pages
367-380
Date Issued
2001
Author(s)
Hacon, C. D.
Abstract
Let X be a smooth complex projective algebraic variety of maximal Albanese dimension. We give a characterization of κ(X) in terms of the set V0(X, ωX) := {P ∈ Pic0(X)|h0(X, ωX ⊗ P) ≠ 0}. An immediate consequence of this is that the Kodaira dimension κ(X) is invariant under smooth deformations. We then study the pluricanonical maps φm : X → ℙ(H0(X, mKX)). We prove that if X is of general type, φm is generically finite for m ≥ 5 and birational for m ≥ 5dim(X) + 1. More generally, we show that for m ≥ 6 the image of φm is of dimension equal to κ(X) and for m ≥ 6κ(X) + 2, φm is the stable canonical map. © Springer-Verlag 2001.
Type
journal article