Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields

Frédéric Campana; Henri Guenancia; Mihai Păun

Annales scientifiques de l'École Normale Supérieure (2013)

  • Volume: 46, Issue: 6, page 879-916
  • ISSN: 0012-9593

Abstract

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We prove the existence of non-positively curved Kähler-Einstein metrics with cone singularities along a given simple normal crossing divisor of a compact Kähler manifold, under a technical condition on the cone angles, and we also discuss the case of positively-curved Kähler-Einstein metrics with cone singularities. As an application we extend to this setting classical results of Lichnerowicz and Kobayashi on the parallelism and vanishing of appropriate holomorphic tensor fields.

How to cite

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Campana, Frédéric, Guenancia, Henri, and Păun, Mihai. "Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields." Annales scientifiques de l'École Normale Supérieure 46.6 (2013): 879-916. <http://eudml.org/doc/272204>.

@article{Campana2013,
abstract = {We prove the existence of non-positively curved Kähler-Einstein metrics with cone singularities along a given simple normal crossing divisor of a compact Kähler manifold, under a technical condition on the cone angles, and we also discuss the case of positively-curved Kähler-Einstein metrics with cone singularities. As an application we extend to this setting classical results of Lichnerowicz and Kobayashi on the parallelism and vanishing of appropriate holomorphic tensor fields.},
author = {Campana, Frédéric, Guenancia, Henri, Păun, Mihai},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {kähler-Einstein metrics; cone singularities; orbifold tensors; Monge-ampère equations},
language = {eng},
number = {6},
pages = {879-916},
publisher = {Société mathématique de France},
title = {Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields},
url = {http://eudml.org/doc/272204},
volume = {46},
year = {2013},
}

TY - JOUR
AU - Campana, Frédéric
AU - Guenancia, Henri
AU - Păun, Mihai
TI - Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2013
PB - Société mathématique de France
VL - 46
IS - 6
SP - 879
EP - 916
AB - We prove the existence of non-positively curved Kähler-Einstein metrics with cone singularities along a given simple normal crossing divisor of a compact Kähler manifold, under a technical condition on the cone angles, and we also discuss the case of positively-curved Kähler-Einstein metrics with cone singularities. As an application we extend to this setting classical results of Lichnerowicz and Kobayashi on the parallelism and vanishing of appropriate holomorphic tensor fields.
LA - eng
KW - kähler-Einstein metrics; cone singularities; orbifold tensors; Monge-ampère equations
UR - http://eudml.org/doc/272204
ER -

References

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