Weil-Petersson Volumes of the Moduli Spaces of CY Manifolds
Andrey Todorov

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.
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Taxonomy
TopicsGeometry and complex manifolds · Algebraic Geometry and Number Theory · Geometric Analysis and Curvature Flows
