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Flips for 3-folds and 4-folds$
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Alessio Corti

Print publication date: 2007

Print ISBN-13: 9780198570615

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198570615.001.0001

Kodaira's canonical bundle formula and adjunction

Chapter:
(p. 134 ) 8 Kodaira's canonical bundle formula and adjunction
Source:
Flips for 3-folds and 4-folds
Author(s):

János Kollár

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198570615.003.0008

If (X,B) is a log canonical pair, it is natural to study the locus nklt(X,B) of points where the pair is not klt. In particular, this chapter proves Kawamata's adjunction formula: if W is an irreducible subvariety of nklt(X,B), then the restriction of K+B to W is expressed naturally in terms of the canonical class of W. This topic provides a simultaneous generalization of the classical adjunction formula, the formula for the canonical class of a smooth blow up, and Kodaira's formula for the canonical class of a relatively minimal elliptic surface. The ideas have many applications in higher dimensional algebraic geometry.

Keywords:   non-klt locus, lc centre, Kawamata, codimension one adjunction formula, Iitaka program, log canonical normalization, log canonical purity, tie-breaking method

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