Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields  [ Métriques à singularités coniques le long de diviseurs à croisements normaux et champs de tenseurs holomorphes ]
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 46 (2013) no. 6, pp. 879-916.

Dans cet article, nous prouvons l'existence de métriques de Kähler-Einstein à courbure négative ayant des singularités coniques le long d'un diviseur à croisements normaux simples sur une variété kählérienne compacte, sous une hypothèse technique sur les angles des cones. Nous discutons également du cas des métriques de Kähler-Einstein à courbure strictement positive avec des singularités coniques. Nous en déduisons que les résultats classiques de Lichnerowicz et Kobayashi sur le parallélisme et l'annulation des champs de tenseurs holomorphes s'étendent à notre cadre.

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.

DOI : https://doi.org/10.24033/asens.2205
Classification : 32Q05,  32Q10,  32Q15,  32Q20,  32U05,  32U15
Mots clés : métriques de kähler-Einstein, singularités coniques, tenseurs orbifoldes, équation de Monge-ampère
@article{ASENS_2013_4_46_6_879_0,
     author = {Campana, Fr\'ed\'eric and Guenancia, Henri and P\u aun, Mihai},
     title = {Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {879--916},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {Ser. 4, 46},
     number = {6},
     year = {2013},
     doi = {10.24033/asens.2205},
     language = {en},
     url = {www.numdam.org/item/ASENS_2013_4_46_6_879_0/}
}
Campana, Frédéric; Guenancia, Henri; Păun, Mihai. Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 46 (2013) no. 6, pp. 879-916. doi : 10.24033/asens.2205. http://www.numdam.org/item/ASENS_2013_4_46_6_879_0/

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