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2012 | 10 | 3 | 885-902
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Weakly-exceptional quotient singularities

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A singularity is said to be weakly-exceptional if it has a unique purely log terminal blow-up. In dimension 2, V. Shokurov proved that weakly-exceptional quotient singularities are exactly those of types D n, E 6, E 7, E 8. This paper classifies the weakly-exceptional quotient singularities in dimensions 3 and 4.
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Bibliografia
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  • [4] Cheltsov I., Log canonical thresholds of del Pezzo surfaces, Geom. Funct. Anal., 2008, 18(4), 1118–1144 http://dx.doi.org/10.1007/s00039-008-0687-2
  • [5] Chel’tsov I., Shramov C., Log canonical thresholds of smooth Fano threefolds, Russian Math. Surveys, 2008, 63(5), 859–958 http://dx.doi.org/10.1070/RM2008v063n05ABEH004561
  • [6] Cheltsov I., Shramov C., On exceptional quotient singularities, Geom. Topol., 2011, 15(4), 1843–1882 http://dx.doi.org/10.2140/gt.2011.15.1843
  • [7] Cheltsov I., Shramov C., Six-dimensional exceptional quotient singularities, preprint avaialble at http://arxiv.org/pdf/1001.3863.pdf
  • [8] Demailly J.-P., On Tian’s invariant and log canonical thresholds, Appendix to: Chel’tsov I., Shramov C., Log canonical thresholds of smooth Fano threefolds, Russian Math. Surveys, 2008, 63(5), 859–958 http://dx.doi.org/10.1070/RM2008v063n05ABEH004561
  • [9] Dolgachev I.V., Iskovskikh V.A., Finite subgroups of the plane Cremona group, In: Algebra, Arithmetic, and Geometry. I, Progr. Math., 269, Birkhäuser, Boston, 443–548
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  • [14] Iskovskikh V.A., Prokhorov Y.G., Fano Varieties, In: Algebraic Geometry, 5, Encyclopaedia Math. Sci., 47, Springer, Berlin, 1999
  • [15] Kollár J., Singularities of pairs, In: Algebraic Geometry, Santa Cruz, July 9–29, 1995, Proc. Sympos. Pure Math., 62(1), American Mathematical Society, Providence, 1997, 221–287
  • [16] Kudryavtsev S.A., Pure log terminal blow-ups, Math. Notes, 2001, 69(5–6), 814–819 http://dx.doi.org/10.1023/A:1010234532502
  • [17] Markushevich D., Prokhorov Yu.G., Exceptional quotient singularities, Amer. J. Math., 1999, 121(6), 1179–1189 http://dx.doi.org/10.1353/ajm.1999.0044
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  • [19] Prokhorov Yu.G., Blow-ups of canonical singularities, In: Proceedings of the International Algebraic Conference held on the occasion of the 90th birthday of A.G.Kurosh, Moscow, May 25–30, 1998, Walter de Gruyter, Berlin, 2000, 301–317
  • [20] Prokhorov Yu.G., Sparseness of exceptional quotient singularities, Math. Notes, 2000, 68(5–6), 664–667 http://dx.doi.org/10.1023/A:1026636027672
  • [21] Segre B., The Non-Singular Cubic Surfaces, Oxford University Press, Oxford, 1942
  • [22] Shokurov V.V., 3-fold log flips, Russian Acad. Sci. Izv. Math., 1993, 40(1), 95–202 http://dx.doi.org/10.1070/IM1993v040n01ABEH001862
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  • [26] Yau S.S.-T., Yu Y., Gorenstein Quotient Singularities in Dimension Three, Mem. Amer. Math. Soc., 505, American Mathematical Society, Providence, 1993
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Bibliografia
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bwmeta1.element.doi-10_2478_s11533-012-0019-5
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