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Log-canonical thresholds on del Pezzo surfaces of degrees ≥ 2

Published online by Cambridge University Press:  11 January 2016

Jihun Park  and
Joonyeong Won
Jihun Park
Affiliation:
Department of Mathematics, Pohang University of Science and Technology, Pohang, Kyungbuk 790-784, Republic of Korea, wlog@postech.ac.kr
Joonyeong Won
Affiliation:
Korea Institute for Advanced Study, Dongdaemun-gu, Seoul 130-722, Republic of Korea, leonwon@kias.re.kr
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Abstract

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We compute the global log-canonical thresholds (lct) of del Pezzo surfaces of degrees ≥ 2 with du Val singularities.

Keywords

14J2614J17
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 200 , December 2010 , pp. 1 - 26
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2010

References

[1] Alexeev, V. and V. Nikulin, Del Pezzo and K3 surfaces, MSJ Mem. 15, Math. Soc. Japan, Tokyo, 2006.Google Scholar
[2] Cheltsov, I., Log canonical thresholds of del Pezzo surfaces, Geom. Funct. Anal. 18 (2008), 1118–1144.CrossRefGoogle Scholar
[3] Cheltsov, I., On singular cubic surfaces, Asian J. Math. 13 (2009), 191–214.CrossRefGoogle Scholar
[4] Cheltsov, I. and Shramov, K., Log-canonical thresholds of smooth Fano threefolds, Russian Math. Surveys 63, no. 5 (2008), 859–958.CrossRefGoogle Scholar
[5] Coray, D. F. and Tsfasman, M. A., Arithmetic on singular del Pezzo surfaces, Proc. Lond. Math. Soc. (3) 57 (1988), 25–87.CrossRefGoogle Scholar
[6] Demailly, J.-P. and Kollár, J., Semi-continuity of complex singularity exponents and Kähler-Einstein metrics on Fano orbifolds, Ann. Sci. Ecole Norm. Sup. (4) 34 (2001), 525–556.CrossRefGoogle Scholar
[7] Demazure, M., “Surfaces de del Pezzo” in Séminaire sur les singularités des surfaces (Palaiseau, France, 1977), Lecture Notes in Math. 777, Springer, Berlin, 1980, 21–69.CrossRefGoogle Scholar
[8] Kollár, J., “Adjunction and discrepancies” in Flips and Abundance for Algebraic Threefolds (Salt Lake City, 1991), Astérisque 211, Soc. Math. France, Paris, 1992, 183–192.Google Scholar
[9] Kosta, D., Del Pezzo surfaces with Du Val singularities, Ph.D. dissertation, University of Edinburgh, Edinburgh, 2009, arXiv:0904.0943v2 [math.AG]Google Scholar
[10] Park, J., Birational maps of del Pezzo fibrations, J. Reine Angew. Math. 538 (2001), 213–221.Google Scholar
[11] Park, J., A note on del Pezzo fibrations of degree 1, Comm. Algebra 31 (2003), 5755–5768.CrossRefGoogle Scholar
[12] Park, J. and Won, J., Log canonical thresholds on Gorenstein canonical del Pezzo surfaces, to appear in Proc. Edinb. Math. Soc., preprint, arXiv:0904.4513 [math.AG] Google Scholar
[13] Pinkham, H. C., “Simple elliptic singularities, del Pezzo surfaces and Cremona transformations” in Several Complex Variables (Williamstown, Mass., 1975), Proc. Sympos. Pure Math. 30, Amer. Math. Soc., Providence, 1977, 69–70.Google Scholar
[14] Pukhlikov, A. V., Birational geometry of Fano direct products, Izv. Math. 69, no. 6 (2005), 1225–1255.CrossRefGoogle Scholar
[15] Urabe, T., “On singularities on degenerate del Pezzo surfaces of degree 1, 2” in Singularities, Part 2 (Arcata, Calif., 1981), Proc. Sympos. Pure Math. 40, Amer. Math. Soc., Providence, 1983, 587–591.Google Scholar