Abstract
Let E be a positive line bundle over a compact complex manifold. We show that the distortion function defined by the quotient of the initial metric by the Fubini-Study metric of E ⊗k admits an equivalent when k tends to infinity. This improves the previous inequalities given by Kempf and Ji over Abelian varieties, and extends them to any projective manifold. The proof rests upon the computation of an equivalent for the heat kernel, with control of the convergence with respect to the time parameter.
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