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

Xu Wang

arxiv: 1607.03265 · v1 · pith:U6ISTHBTnew · submitted 2016-07-12 · 🧮 math.CV · math.AG· math.DG

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

Xu Wang This is my paper

classification 🧮 math.CV math.AGmath.DG

keywords mathcalapplicationcriteriondirectimagemetricnegative-curvatureshall

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We shall show that $q$-semipositivity of the vector bundle $E$ over a K\"ahler 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.

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