Kähler-Einstein metrics with mixed Poincaré and cone singularities along a normal crossing divisor
[Métriques de Kähler-Einstein à singularités mixtes Poincaré et coniques le long d’un diviseur à croisements normaux]
Guenancia, Henri
Annales de l'Institut Fourier, Tome 64 (2014), p. 1291-1330 / Harvested from Numdam
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Soit X une variété compacte kählerienne et Δ un ℝ-diviseur dont le support est à croisements normaux simples et à coefficients entre 1/2 et 1. En supposant K X +Δ ample, on prouve l’existence et l’unicité d’une métrique de Kähler-Einstein à courbure négative sur X∖Supp(Δ) ayant des singularités mixtes Poincaré et coniques suivant les coefficients de Δ. Nous appliquons ensuite ce résultat pour prouver un théorème d’annulation concernant certains champs de tenseurs holomorphes naturellement attachés à la paire (X,Δ).

Let X be a compact Kähler manifold and Δ be a ℝ-divisor with simple normal crossing support and coefficients between 1/2 and 1. Assuming that K X +Δ is ample, we prove the existence and uniqueness of a negatively curved Kahler-Einstein metric on X∖Supp(Δ) having mixed Poincaré and cone singularities according to the coefficients of Δ. As an application we prove a vanishing theorem for certain holomorphic tensor fields attached to the pair (X,Δ).

Publié le : 2014-01-01
DOI : https://doi.org/10.5802/aif.2881
Classification:  32Q05,  32Q10,  32Q15,  32Q20,  32U05,  32U15
Mots clés: métriques de Kähler-Einstein, singularités coniques, singularités Poincaré, cusps, tenseurs orbifoldes, équation de Monge-Ampère complexe 
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     author = {Guenancia, Henri},
     title = {K\"ahler-Einstein metrics with mixed Poincar\'e and cone singularities along a normal crossing divisor},
     journal = {Annales de l'Institut Fourier},
     volume = {64},
     year = {2014},
     pages = {1291-1330},
     doi = {10.5802/aif.2881},
     zbl = {06387308},
     mrnumber = {3330171},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2014__64_3_1291_0}
}

Guenancia, Henri. Kähler-Einstein metrics with mixed Poincaré and cone singularities along a normal crossing divisor. Annales de l'Institut Fourier, Tome 64 (2014) pp. 1291-1330. doi : 10.5802/aif.2881. http://gdmltest.u-ga.fr/item/AIF_2014__64_3_1291_0/

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