Abstract
The purpose of this chapter is to discuss “base point freeness” of linear systems of adjoint type, i.e., linear systems of type \( \left| {K_x + B} \right|, \), where K X denotes the canonical divisor of a variety X and B is a (boundary) divisor with some specific conditions depending on the situation. As is clear from the formulation, the most natural framework for linear systems of adjoing type is that of the logarithmic category discussed in Chapter 2. Our key tool is the logarithmic version of the Kodaira vanishing theorem, i.e., the Kawamata—Viehweg vanishing theorem. Our viewpoint centering on adjoint linear systems, is in the spirit of Ein—Lazarsfeld [1], which applied the method of Kawamata—Reid—Shokurov to solve Fujita’s conjecture in dimension 3.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media New York
About this chapter
Cite this chapter
Matsuki, K. (2002). Base Point Freeness of Adjoint Linear Systems. In: Introduction to the Mori Program. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-5602-9_7
Download citation
DOI: https://doi.org/10.1007/978-1-4757-5602-9_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3125-2
Online ISBN: 978-1-4757-5602-9
eBook Packages: Springer Book Archive