Kähler-Einstein metrics on complex surfaces with \(C_ 1>0\). (English) Zbl 0631.53052
On donne des diverses estimations de la limite inférieure de l’invariant holomorphique \(\alpha (M)\), défini dans [le premier auteur, Invent. Math. 89, 225–246 (1987; Zbl 0599.53046)], par l’utilisation du recouvrement ramifié, des estimations de potentiel et des nombres de Lelong de type positif d-fermés, et des courants de type défini. Ces estimations sont appliquées à la construction des métriques Kähler-Einstein sur des surfaces complexes avec \(C_ 1>0\), et on montre qu’il existe de telles structures sur toute variété du type différentiel \(\mathbb CP^ 2\#\overline{n\mathbb CP^ 2}\) \((3\leq n\leq 8)\).
Reviewer: V.Obadeanu
MSC:
| 53C55 | Global differential geometry of Hermitian and Kählerian manifolds |
| 53C15 | General geometric structures on manifolds (almost complex, almost product structures, etc.) |
| 32Q20 | Kähler-Einstein manifolds |
Keywords:
holomorphic invariant; Lelong numbers; branched coverings; currents; Kähler-Einstein metrics; complex surfaces; gravitational instantonsReferences:
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