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It is known that the integrations of Ricci curvature of the Weil-Petersson metric on the moduli space of Calabi-Yau varieties is a rational numbers

My question is about the moduli space of varieties of general type (varieties with negative first Chern class) we have again Weil Petersson metric and so the integrations of Ricci curvature of the Weil-Petersson metric on the moduli space of varieties of general type is a rational numbers?

$$\int_M\omega_{WP}^m\in \mathbb Q$$

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