Abstract
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.
| Original language | English (US) |
|---|---|
| Title of host publication | Flips for 3-folds and 4-folds |
| Publisher | Oxford University Press |
| ISBN (Electronic) | 9780191717703 |
| ISBN (Print) | 9780198570615 |
| DOIs | |
| State | Published - Sep 1 2007 |
All Science Journal Classification (ASJC) codes
- General Mathematics
Keywords
- Codimension one adjunction formula
- Iitaka program
- Kawamata
- Lc centre
- Log canonical normalization
- Log canonical purity
- Non-klt locus
- Tie-breaking method
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