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Exponential estimate for the asymptotics of Bergman kernels


We prove an exponential estimate for the asymptotics of Bergman kernels of a positive line bundle under hypotheses of bounded geometry. Further, we give Bergman kernel proofs of complex geometry results, such as separation of points, existence of local coordinates and holomorphic convexity by sections of positive line bundles.

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Correspondence to George Marinescu.

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X. Ma: Partially supported by Institut Universitaire de France and funded through the Institutional Strategy of the University of Cologne within the German Excellence Initiative.

G. Marinescu: Partially supported by DFG funded projects SFB/TR 12, MA 2469/2-1 and ENS Paris.

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Ma, X., Marinescu, G. Exponential estimate for the asymptotics of Bergman kernels. Math. Ann. 362, 1327–1347 (2015).

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