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Semi-Normal Log Centres and Deformations of Pairs

Published online by Cambridge University Press:  19 December 2013

János Kollár
János Kollár*
Affiliation:
Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544-1000, USA ([email protected])
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Abstract

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We show that some of the properties of log canonical centres of a log canonical pair also hold for certain subvarieties that are close to being a log canonical centre. As a consequence, we obtain that, in working with deformations of pairs where all the coefficients of the boundary divisor are bigger than ½, embedded points never appear on the boundary divisor.

Keywords

log canonical centresemi-normalitydeformation of pairsPrimary 14J1514J1714E3014C20
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 57 , Issue 1 , February 2014 , pp. 191 - 199
Copyright
Copyright © Edinburgh Mathematical Society 2014 

References

1.Ambro, F., On minimal log discrepancies, Math. Res. Lett. 6(5) (1999), 573–580.Google Scholar
2.Ambro, F., Quasi-log varieties, Tr. Mat. Inst. Steklova 240 (2003), 220–239.Google Scholar
3.Ambro, F., Basic properties of log canonical centers, in Classification of algebraic varieties, European Mathematical Society Series of Congress Reports, pp. 39–48 (European Mathematical Society, Zürich, 2011).Google Scholar
4.Birkar, C., Existence of log canonical flips and a special LMMP, Publ. Math. IHES 115(1) (2012), 325–368.CrossRefGoogle Scholar
5.Birkar, C., Cascini, P., Hacon, C. D. and McKernan, J., Existence of minimal models for varieties of log general type, J. Am. Math. Soc. 23(2) (2010), 405–468.CrossRefGoogle Scholar
6.Fujino, O., Introduction to the log minimal model program for log canonical pairs, eprint (arXiv:0907.1506, 2009).Google Scholar
7.Fujino, O., Semi-stable minimal model program for varieties with trivial canonical divisor, Proc. Jpn Acad. A 87(3) (2011), 25–30.Google Scholar
8.Hacon, C. D. and Xu, C., Existence of log canonical closures, Invent. Math. 192(1) (2013), 161–195.CrossRefGoogle Scholar
9.Kawamata, Y., Subadjunction of log canonical divisors, II, Am. J. Math. 120(5) (1998), 893–899.Google Scholar
10.Kollár, J., Flips and abundance for algebraic threefolds, Flips and abundance for algebraic threefolds, Volume 211 (Société Mathématique de France, Paris, 1992).Google Scholar
11.Kollár, J., Rational curves on algebraic varieties, Rational curves on algebraic varieties, Volume 32 (Springer, 1996).Google Scholar
12.Kollár, J., Singularities of pairs, in Algebraic geometry: Santa Cruz 1995, American Mathematical Society Translations, Volume 62, pp. 221–287 (American Mathematical Society, Providence, RI, 1997).Google Scholar
13.Kollár, J., Which powers of holomorphic functions are integrable?, eprint (arXiv: 0805.0756, 2008).Google Scholar
14.Kollár, J., Moduli of varieties of general type, in Handbook of moduli: parameter spaces of curves (ed. Farkas, G. and Morrison, I.) (International Press, Somerville, MA, 2013).Google Scholar
15.Kollár, J., Singularities of the minimal model program, Cambridge Tracts in Mathematics, Volume 200 (Cambridge University Press, 2013).CrossRefGoogle Scholar
16.Kollár, J. and Kovács, S. J., Log canonical singularities are Du Bois, J. Am. Math. Soc. 23(3) (2010), 791–813.CrossRefGoogle Scholar
17.Kollár, J. and Mori, S., Birational geometry of algebraic varieties, Cambridge Tracts in Mathematics, Volume 134 (Cambridge University Press, 1998).Google Scholar
18.Kovács, S. J., Schwede, K. and Smith, K. E., The canonical sheaf of Du Bois singularities, Adv. Math. 224(4) (2010), 1618–1640.CrossRefGoogle Scholar
19.Prokhorov, Y. G., Lectures on complements on log surfaces, Mathematical Society of Japan Memoirs, Volume 10 (Mathematical Society of Japan, Tokyo, 2001).Google Scholar
20.Shokurov, V. V., Three-dimensional log perestroikas, Izv. Ross. Akad. Nauk Ser. Mat. 56(1) (1992), 105–203.Google Scholar
21.Shokurov, V. V., Letters of a bi-rationalist, VII, Ordered termination, Tr. Mat. Inst. Steklova 264 (2009), 184–208.Google Scholar