Kähler-Einstein metrics on log del Pezzo surfaces in weighted projective 3-spaces
[Métriques de Kähler-Einstein sur les surfaces de del Pezzo logarithmiques dans les espaces projectifs à poids de dimension 3]
Annales de l'Institut Fourier, Tome 51 (2001) no. 1, pp. 69-79.

Nous déterminons toutes les surfaces de del Pezzo logarithmiques quasi-lisses dans les espaces projectifs à poids de dimension 3, qui sont plongées par leur morphisme anticanonique. Beaucoup de ces surfaces admettent une métrique de Kähler-Einstein, et la plupart de celles-ci n'ont pas de tigres.

We determine all anticanonically embedded quasi smooth log del Pezzo surfaces in weighted projective 3-spaces. Many of these admit a Kähler-Einstein metric and most of them do not have tigers.

DOI : 10.5802/aif.1815
Classification : 14J26, 14Q10, 32Q20
Keywords: del Pezzo surface, Kähler-Einstein metric
Mot clés : surface de del Pezzo, métrique de Kähler-Einstein
Johnson, Jennifer M. 1 ; Kollár, János 1

1 Princeton University, Department of Mathematics, Fine Hall, Washington Road, Princeton NJ 08544-1000 (USA)
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     title = {K\"ahler-Einstein metrics on log del {Pezzo} surfaces in weighted projective 3-spaces},
     journal = {Annales de l'Institut Fourier},
     pages = {69--79},
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Johnson, Jennifer M.; Kollár, János. Kähler-Einstein metrics on log del Pezzo surfaces in weighted projective 3-spaces. Annales de l'Institut Fourier, Tome 51 (2001) no. 1, pp. 69-79. doi : 10.5802/aif.1815. http://www.numdam.org/articles/10.5802/aif.1815/

[Al1] V. Alexeev Two two-dimensional terminations, Duke Math. J., Volume 69 (1993), pp. 527-545 | DOI | MR | Zbl

[Al2] V. Alexeev Boundedness and K 2 for log surfaces, Internat. J. Math., Volume 5 (1994), pp. 779-810 | DOI | MR | Zbl

[BoGa] C. Boyer; K. Galicki New Einstein Manifolds in Dimension Five (Manuscript)

[Br] E. Brieskorn Rationale Singularitäten komplexer Flächen, Invent. Math., Volume 4 (1968), pp. 336-358 | DOI | MR | Zbl

[DeKo] J.-P. Demailly; J. Kollár Semi-continuity of complex singularity exponents and Kähler-Einstein metrics on Fano orbifolds (To appear) | Numdam | MR | Zbl

[Do] I. Dolgachev Weighted projective varieties, Group actions and vector fields (Lecture Notes in Math.), Volume vol. 956 (1982), pp. 34-71 | Zbl

[Fl] A.R. Fletcher Working with weighted complete intersections (1989) (Preprint MPI/89-35, Max-Planck Institut für Mathematik, Bonn)

[Fu] W. Fulton Intersection theory, Springer-Verlag, 1984, Berlin-New York, 1998 | MR | Zbl

[KeMcK] S. Keel; J. McKernan Rational curves on quasi-projective surfaces, Mem. Amer. Math. Soc., Volume 140 (1999) no. 669 | MR | Zbl

[Ko] J. Kollár Singularities of pairs, Algebraic Geometry, Santa Cruz, 1995 (Proceedings of Symposia in Pure Math.), Volume vol. 62 (1997), pp. 221-287 | Zbl

[KoMo] J. Kollár; S. Mori Birational geometry of algebraic varieties, Cambridge Univ. Press, 1998 | MR | Zbl

[Mi] M. Miyanishi Non complete algebraic surfaces, Lecture Notes in Mathematics, 857, Springer-Verlag, Berlin-New York, 1981 | MR | Zbl

[Na] A.M. Nadel Multiplier ideal sheaves and Kähler-Einstein metrics of positive scalar curvature, Annals of Math., Volume 132 (1990), pp. 549-596 | DOI | MR | Zbl

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