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Five-Dimensional Weakly Exceptional Quotient Singularities

Published online by Cambridge University Press:  23 December 2013

Dmitrijs Sakovics
Dmitrijs Sakovics*
Affiliation:
School of Mathematics, James Clerk Maxwell Building, University of Edinburgh, King's Buildings, Edinburgh EH9 3JZ, UK ([email protected])
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Abstract

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A singularity is said to be weakly exceptional if it has a unique purely log terminal blow-up. This is a natural generalization of the surface singularities of types Dn, E6, E7 and E8. Since this idea was introduced, quotient singularities of this type have been classified in dimensions up to at most 4. This note extends that classification to dimension 5.

Keywords

singularitiesquotient singularitiesweakly exceptionalPrimary 14B05Secondary 14E07
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 57 , Issue 1 , February 2014 , pp. 269 - 279
Copyright
Copyright © Edinburgh Mathematical Society 2014 

References

1.Adler, A., On the automorphism group of a certain cubic threefold, Am. J. Math. 100(6) (1978), 1275–1280.Google Scholar
2.Burkhardt, H., Untersuchungen aus dem Gebiete der hyperelliptischen Modulfunctionen, Math. Ann. 38(2) (1891), 161–224.CrossRefGoogle Scholar
3.Cheltsov, I. and Shramov, C., Weakly-exceptional singularities in higher dimensions, J. Reine Angew. Math. (in press).Google Scholar
4.Cheltsov, I. and Shramov, C., On exceptional quotient singularities, Geom. Topol. 15 (2011), 1843–1882.Google Scholar
5.Feit, W., The current situation in the theory of finite simple groups, in Actes du Congres International des Mathématiciens, Nice, 1970, Volume 1, pp. 55–93 (Gauthier–Villars, Paris, 1970).Google Scholar
6.González-Aguilera, V. and Liendo, A., On the order of an automorphism of a smooth hypersurface, Israel J. Math. 197(1) (2013), 29–49.CrossRefGoogle Scholar
7.Höfling, B., Finite irreducible imprimitive nonmonomial complex linear groups of degree 4, J. Alg. 236(2) (2001), 419–470.CrossRefGoogle Scholar
8.Kudryavtsev, S. A., Pure log terminal blow-ups, Math. Notes 69(5) (2001), 814–819.Google Scholar
9.Mumford, D. and Horrocks, G., A rank 2 vector bundle on ℙ4 with 15 000 symmetries, Topology 12 (1973), 63–81.Google Scholar
10.Sakovics, D., Weakly-exceptional quotient singularities, Central Eur. J. Math. 10(3) (2012), 885–902.CrossRefGoogle Scholar
11.Shokurov, V. V., 3-fold log flips, Russ. Ac. SC Izv. Math. 40(1) (1993), 95–202.Google Scholar
12.Springer, T. A., Invariant theory, Lecture Notes in Mathematics, Volume 585 (Springer, 1977).Google Scholar
13.Swallow, J., Exploratory Galois theory (Cambridge University Press, 2004).Google Scholar