Kähler-Einstein metrics singular along a smooth divisor

Raffe Mazzeo

Journées équations aux dérivées partielles (1999)

  • page 1-10
  • ISSN: 0752-0360

Abstract

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In this note we discuss some recent and ongoing joint work with Thalia Jeffres concerning the existence of Kähler-Einstein metrics on compact Kähler manifolds which have a prescribed incomplete singularity along a smooth divisor D . We shall begin with a general discussion of the problem, and give a rough outline of the “classical” proof of existence in the smooth case, due to Yau and Aubin, where no singularities are prescribed. Following this is a discussion of the geometry of the conical or edge singularities and then some discussion of the new elements of the proof in this context.

How to cite

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Mazzeo, Raffe. "Kähler-Einstein metrics singular along a smooth divisor." Journées équations aux dérivées partielles (1999): 1-10. <http://eudml.org/doc/93383>.

@article{Mazzeo1999,
abstract = {In this note we discuss some recent and ongoing joint work with Thalia Jeffres concerning the existence of Kähler-Einstein metrics on compact Kähler manifolds which have a prescribed incomplete singularity along a smooth divisor $D$. We shall begin with a general discussion of the problem, and give a rough outline of the “classical” proof of existence in the smooth case, due to Yau and Aubin, where no singularities are prescribed. Following this is a discussion of the geometry of the conical or edge singularities and then some discussion of the new elements of the proof in this context.},
author = {Mazzeo, Raffe},
journal = {Journées équations aux dérivées partielles},
keywords = {Kähler-Einstein metrics; compact Kähler manifolds; incomplete singularity along a smooth divisor},
language = {eng},
pages = {1-10},
publisher = {Université de Nantes},
title = {Kähler-Einstein metrics singular along a smooth divisor},
url = {http://eudml.org/doc/93383},
year = {1999},
}

TY - JOUR
AU - Mazzeo, Raffe
TI - Kähler-Einstein metrics singular along a smooth divisor
JO - Journées équations aux dérivées partielles
PY - 1999
PB - Université de Nantes
SP - 1
EP - 10
AB - In this note we discuss some recent and ongoing joint work with Thalia Jeffres concerning the existence of Kähler-Einstein metrics on compact Kähler manifolds which have a prescribed incomplete singularity along a smooth divisor $D$. We shall begin with a general discussion of the problem, and give a rough outline of the “classical” proof of existence in the smooth case, due to Yau and Aubin, where no singularities are prescribed. Following this is a discussion of the geometry of the conical or edge singularities and then some discussion of the new elements of the proof in this context.
LA - eng
KW - Kähler-Einstein metrics; compact Kähler manifolds; incomplete singularity along a smooth divisor
UR - http://eudml.org/doc/93383
ER -

References

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  14. [14] G. Tian and S.T. Yau, Existence of Kähler-Einstein metrics on complete Kähler manifolds and their applications to algebraic geometry, in Mathematical Aspects of String Theory (S.T. Yau, ed.), World Scientific (1987), 574-628. Zbl0682.53064MR915840
  15. [15] G. Tian and S.T. Yau, Complete Kähler manifolds with zero Ricci curvature I, J. Amer. Math. Soc., 3 No. 3 (1990), 579-609. Zbl0719.53041MR91a:53096
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