Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-02-05T17:22:48.692Z Has data issue: false hasContentIssue false
  • English
  • Français

Log del Pezzo Surfaces with Simple Automorphism Groups

Published online by Cambridge University Press:  10 December 2014

Grigory Belousov
Grigory Belousov*
Affiliation:
Flat 51, House 21-2, 3-d Rybinskay Street, 107113 Moscow, Russian Federation, ([email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In the present paper we classify del Pezzo surfaces with log terminal singularities admitting an action of a finite simple group.

Keywords

del Pezzo surfacesCremona groupbirational automorphismsPrimary 14J2614J4514J50
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 58 , Issue 1 , February 2015 , pp. 33 - 52
Copyright
Copyright © Edinburgh Mathematical Society 2015 

References

1.Alexeev, V., Theorems about good divisors on log Fano varieties (case of index r > n – 2), in Algebraic geometry, Lecture Notes in Mathematics, Volume 1479, pp. 1–9 (Springer, 1989).Google Scholar
2.Alexeev, V., Two 2-dimensional terminations, Duke Math. J. 69(3) (1993), 527–545.CrossRefGoogle Scholar
3.Alexeev, V. and Nikulin, V, Del Pezzo and K3 surfaces, Mathematical Society of Japan Memoirs, Volume 15 (Japan Mathematical Society, Tokyo, 2006).Google Scholar
4.Belousov, G., The maximal number of singular points on log del Pezzo surfaces, J. Math. Sci. Univ. Tokyo 16 (2009), 1–8.Google Scholar
5.Brieskorn, E., Rationale singularitaten komplexer Flbächen, Invent. Math. 4 (1968), 336–358.Google Scholar
6.Cheltsov, I., Two local inequalities, Izv. Math. 78 (2014), 375–426.Google Scholar
7.Cheltsov, I. and Shramov, C., Five embeddings of one simple group, Trans. Am. Math. Soc. 366 (2014), 1289–1331.Google Scholar
8.Dolgachev, I. V. and Iskovskikh, V. A., Finite subgroups of the plane Cremona group algebra, in Arithmetic and geometry: Manin Festschrift, Progress in Mathematics, Volume 269, pp. 443–549 (Birkhauser, Boston, MA, 2009).Google Scholar
9.Furushima, M., Singular del Pezzo surfaces and analytic compactifications of 3-dimensional complex affine space C 3, Nagoya Math. J. 104 (1986), 1–28.Google Scholar
10.Hidaka, F. and Watanabe, K., Normal Gorenstein surfaces with ample anti-canonical divisor, Tokyo J. Math. 4 (1981), 319–330.Google Scholar
11.Prokhorov, Y. G., Simple finite subgroups of the Cremona group of rank 3, J. Alg. Geom. 21 (2012), 563–600.CrossRefGoogle Scholar
12.Serre, J.-P., A Minkowski-style bound for the orders of the finite subgroups of the Cremona group of rank 2 over an arbitrary field, Mosc. Math. J. 9(1) (2009), 183–198.Google Scholar
13.Shokurov, V. V., 3-fold log flips, Russ. Acad. Sci. Izv. Math. 40 (1993), 95–202.Google Scholar