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Divisors computing the minimal log discrepancy on a smooth surface

Published online by Cambridge University Press:  13 March 2017

MASAYUKI KAWAKITA
MASAYUKI KAWAKITA*
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan. e-mail: masayuki@kurims.kyoto-u.ac.jp
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Abstract

We study a divisor computing the minimal log discrepancy on a smooth surface. Such a divisor is obtained by a weighted blow-up. There exists an example of a pair such that any divisor computing the minimal log discrepancy computes no log canonical thresholds.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 163 , Issue 1 , July 2017 , pp. 187 - 192
Copyright
Copyright © Cambridge Philosophical Society 2017 

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References

REFERENCES

[1] Abhyankar, S. S. Resolution of singularities of embedded algebraic surfaces. Second edition. Springer Monographs in Mathematics (Springer-Verlag, 1998).Google Scholar
[2] Blum, H. On divisors computing MLD's and LCT's. arXiv:1605.09662.Google Scholar
[3] Hacon, C. D., McKernan, J. and Xu, C. ACC for log canonical thresholds. Ann. of Math. (2) 180 (2014), no. 2, 523–571.Google Scholar
[4] Hironaka, H. Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II. Ann. of Math. (2) 79 (1964), 109–203; ibid. (2) 79 (1964), 205–326.Google Scholar
[5] Kollár, J. Singularities of the minimal model program. Cambridge Tracts in Mathematics 200 (Cambridge University Press, 2013).Google Scholar
[6] Kollár, J., Smith, K. E. and Corti, A. Rational and nearly rational varieties. Cambridge Studies in Advanced Mathematics 92 (Cambridge University Press, 2004).Google Scholar
[7] Shokurov, V. V. Letters of a bi-rationalist. V. Minimal log discrepancies and termination of log flips. Tr. Mat. Inst. Steklova 246 (2004), 328–351; translation in Proc. Steklov Inst. Math. 246 (2004), 315–336.Google Scholar