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Courbure bisectionnelle positive et variétés algébriques affines. (Positive bisectional curvature and affine algebraic varieties). (French) Zbl 0579.53043
Theorem: Let X be a complete Kähler manifold of complex dimension n. Suppose that X has positive bisectional curvature and (i) the volume of the geodesic ball \(B(x_ 0,r)\) is \(\geq\) \(cr^{2n}\), (ii) 0 \(<\) scalar curvature \(<\) \(c/d^ 2(x_ 0,x)\) where d is the geodesic distance. Then X is biholomorphic to an affine algebraic variety.
Reviewer: K.Lai

MSC:
53C55 Global differential geometry of Hermitian and Kählerian manifolds
14A10 Varieties and morphisms
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