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

2016/07/12 by Wang, Xu
#32A25 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1607.03265

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}⊗ E). As an application, we shall give a negative-curvature criterion for the generalized Weil-Petersson metric on the base manifold.

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