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On the Log Canonical Inversion of Adjunction

Published online by Cambridge University Press:  19 December 2013

Christopher D. Hacon
Christopher D. Hacon*
Affiliation:
Department of Mathematics, University of Utah, 155 South 1400 East, JWB 233, Salt Lake City, UT 84112, USA, ([email protected])
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Abstract

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We prove a result on the inversion of adjunction for log canonical pairs that generalizes Kawakita's result to log canonical centres of arbitrary codimension.

Keywords

inversion of adjunctionlog canonical pairsminimal model programPrimary 14E30Secondary 14N3014B05
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 57 , Issue 1 , February 2014 , pp. 139 - 143
Copyright
Copyright © Edinburgh Mathematical Society 2014 

References

1.Ambro, F., The adjunction conjecture and its applications, eprint (arXiv:9903060v3, 1999).Google Scholar
2.Ambro, F., Shokurov's boundary property, J. Diff. Geom. 67(2) (2004), 229–255.Google Scholar
3.Birkar, C., Cascini, P., Hacon, C. and McKernan, J., Existence of minimal models for varieties of log general type, J. Am. Math. Soc. 23(2) (2010), 405–468.CrossRefGoogle Scholar
4.Corti, A., 3-fold flips after Shokurov, in Flips for 3-folds and 4-folds, Oxford Lecture Series in Mathematics and Its Applications, Volume 35 (Oxford University Press, 2007).CrossRefGoogle Scholar
5.Fujino, O., Special termination and reducion to pl-flips, in Flips for 3-folds and 4-folds, Oxford Lecture Series in Mathematics and Its Applications, Volume 35 (Oxford University Press, 2007).Google Scholar
6.Kawakita, M., Inversion of adjunction on log canonicity, Invent. Math. 167(1) (2007), 129–133.CrossRefGoogle Scholar
7.Kawamata, Y., Subadjunction of log canonical divisors, II, Am. J. Math. 120(5) (1998), 893–899.CrossRefGoogle Scholar
8.Kollár, J., Flips and abundance for algebraic threefolds: a summer seminar at the university of Utah (Salt Lake City, 1991), Astérisque, Volume 211 (Société Mathématique de France, Paris, 1992).Google Scholar
9.Kollár, J., Kodaira's canonical bundle formula and adjunction, in Flips for 3-folds and 4-folds, Oxford Lecture Series in Mathematics and Its Applications, Volume 35, pp. 134–162 (Oxford University Press, 2007).CrossRefGoogle Scholar
10.Kollár, J. and Kovács, S., Log canonical singularities are Du Bois, J. Am. Math. Soc. 23(3) (2010), 791–813.Google Scholar
11.Kollár, J. and Mori, S., Birational geometry of algebraic varieties, Cambridge Tracts in Mathematics, Volume 134 (Cambridge University Press, 1998).CrossRefGoogle Scholar
12.Schwede, K., F-adjunction, Alg. Num. Theory 3(8) (2009), 907–950.CrossRefGoogle Scholar
13.Shokurov, V. V., Semi-stable 3-fold flips, Izv. Ross. Akad. Nauk Ser. Mat. 57(2) (1993), 165–222.Google Scholar