Weil-Petersson Volumes of the Moduli Spaces of CY Manifolds

TL;DR

This paper proves that the volumes of moduli spaces of polarized Calabi-Yau manifolds, measured with the Weil-Petersson metric, are finite and rational, providing important geometric and arithmetic insights.

Contribution

It establishes the finiteness and rationality of Weil-Petersson volumes for moduli spaces of polarized CY manifolds, a novel result in complex geometry.

Findings

Volumes are finite

Volumes are rational numbers

Moduli spaces have well-defined Weil-Petersson volumes

Abstract

In this paper it is proved that the volumes of the moduli spaces of polarized CY manifolds with respect to the Weil-Petersson metrics are finite and they are rational numbers.