Curvature of higher direct image sheaves and its application on negative-curvature criterion for the Weil-Petersson metric

Abstract

We shall show that $q$-semipositivity of the vector bundle $E$ over a Kähler total space $\mathcal{X}$ implies the Griffiths-semipositivity of the $q$-th direct image of $\mathcal{O}(K_{\mathcal{X}/B}\otimes E)$. As an application, we shall give a negative-curvature criterion for the generalized Weil-Petersson metric on the base manifold.

21 pages

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