Kodaira's canonical bundle formula and adjunction

Research output: Chapter in Book/Report/Conference proceedingChapter

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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 languageEnglish (US)
Title of host publicationFlips for 3-folds and 4-folds
PublisherOxford University Press
ISBN (Electronic)9780191717703
ISBN (Print)9780198570615
StatePublished - Sep 1 2007

All Science Journal Classification (ASJC) codes

  • General Mathematics


  • 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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