Kähler-Einstein metrics on log del Pezzo surfaces in weighted projective 3-spaces

Jennifer M. Johnson[1]; János Kollár[1]

  • [1] Princeton University, Department of Mathematics, Fine Hall, Washington Road, Princeton NJ 08544-1000 (USA)

Annales de l’institut Fourier (2001)

  • Volume: 51, Issue: 1, page 69-79
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Johnson, Jennifer M., and Kollár, János. "Kähler-Einstein metrics on log del Pezzo surfaces in weighted projective 3-spaces." Annales de l’institut Fourier 51.1 (2001): 69-79. <http://eudml.org/doc/115914>.

@article{Johnson2001,
abstract = {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.},
affiliation = {Princeton University, Department of Mathematics, Fine Hall, Washington Road, Princeton NJ 08544-1000 (USA); Princeton University, Department of Mathematics, Fine Hall, Washington Road, Princeton NJ 08544-1000 (USA)},
author = {Johnson, Jennifer M., Kollár, János},
journal = {Annales de l’institut Fourier},
keywords = {del Pezzo surface; Kähler-Einstein metric; Fano variety; Kawamata log-terminal; tiger},
language = {eng},
number = {1},
pages = {69-79},
publisher = {Association des Annales de l'Institut Fourier},
title = {Kähler-Einstein metrics on log del Pezzo surfaces in weighted projective 3-spaces},
url = {http://eudml.org/doc/115914},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Johnson, Jennifer M.
AU - Kollár, János
TI - Kähler-Einstein metrics on log del Pezzo surfaces in weighted projective 3-spaces
JO - Annales de l’institut Fourier
PY - 2001
PB - Association des Annales de l'Institut Fourier
VL - 51
IS - 1
SP - 69
EP - 79
AB - 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.
LA - eng
KW - del Pezzo surface; Kähler-Einstein metric; Fano variety; Kawamata log-terminal; tiger
UR - http://eudml.org/doc/115914
ER -

References

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  8. W. Fulton, Intersection theory, (1998), Springer-Verlag, 1984, Berlin-New York Zbl0885.14002MR1644323
  9. S. Keel, J. McKernan, Rational curves on quasi-projective surfaces, Mem. Amer. Math. Soc. 140 (1999) Zbl0955.14031MR1610249
  10. J. Kollár, Singularities of pairs, Algebraic Geometry, Santa Cruz, 1995 vol. 62 (1997), 221-287, AMS Zbl0905.14002
  11. J. Kollár, S. Mori, Birational geometry of algebraic varieties, (1998), Cambridge Univ. Press Zbl0926.14003MR1658959
  12. M. Miyanishi, Non complete algebraic surfaces, 857 (1981), Springer-Verlag, Berlin-New York Zbl0456.14018MR635930
  13. A.M. Nadel, Multiplier ideal sheaves and Kähler-Einstein metrics of positive scalar curvature, Annals of Math. 132 (1990), 549-596 Zbl0731.53063MR1078269

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