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The Weil-Petersson metric is a Kahler metric on the moduli space of Calabi-Yau varieties, the moduli space of general type varieties, the moduli space of K-stable Fano varieties, and more generally, we can define it on the moduli space of stable varieties.
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Ricci curvature of the Weil-Petersson metric?
Let $\omega_{\text{WP}}$ denote the Weil-Petersson metric associated to a family of Calabi-Yau manifolds. That is, let $f : X \to Y$ be a surjective holomorphic map with connected fibres such that, ov …