TY - JOUR

T1 - On the asymptotic behavior of complete kähler metrics of positive Ricci curvature

AU - Anchouche, Boudjemâa

PY - 2010/2

Y1 - 2010/2

N2 - Let (X, g) be a complete noncompact Kähler manifold, of dimension n ≥ 2, with positive Ricci curvature and of standard type (see the definition below). N. Mok proved that X can be compactified, i.e., X is biholomorphic to a quasi-projective variety. The aim of this paper is to prove that the L 2 holomorphic sections of the line bundle Kxq and the volume form of the metric g have no essential singularities near the divisor at infinity. As a consequence we obtain a comparison between the volume forms of the Kahler metric g and of the Fubini-Study metric induced on X. In the case of dimcX = 2, we establish a relation between the number of components of the divisor D and the dimension of the groups H i(X̄,Ω1/X(log D)).

AB - Let (X, g) be a complete noncompact Kähler manifold, of dimension n ≥ 2, with positive Ricci curvature and of standard type (see the definition below). N. Mok proved that X can be compactified, i.e., X is biholomorphic to a quasi-projective variety. The aim of this paper is to prove that the L 2 holomorphic sections of the line bundle Kxq and the volume form of the metric g have no essential singularities near the divisor at infinity. As a consequence we obtain a comparison between the volume forms of the Kahler metric g and of the Fubini-Study metric induced on X. In the case of dimcX = 2, we establish a relation between the number of components of the divisor D and the dimension of the groups H i(X̄,Ω1/X(log D)).

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U2 - 10.4153/CJM-2010-001-0

DO - 10.4153/CJM-2010-001-0

M3 - Article

AN - SCOPUS:76749135828

VL - 62

SP - 3

EP - 18

JO - Canadian Journal of Mathematics

JF - Canadian Journal of Mathematics

SN - 0008-414X

IS - 1

ER -