Variation of Bergman kernels of adjoint line bundles
نویسنده
چکیده
Let f : X −→ S be a smooth projective family and let (L, h) be a singular hermitian line bundle on X with semipositive curvature current. Let Ks := K(Xs, KXs +L | Xs, h | Xs)(s ∈ S) be the Bergman kernel of KXs +L | Xs with respect to h | Xs and let hB the singular hermitian metric on KX + L defined by hB |Xs := 1/Ks. We prove that hB has semipositive curvature. This is a generalization of the recent result of Berndtsson ([B1]). Using this result, we give a new proof of Kawamata’s semipositivity theorem for the direct image of relative multi canonical bundle.
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