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arXiv · 2209.10842

The complex hyperbolic form as a Weil-Petersson form

Xiangsheng Wang
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Abstract

For the moduli space of the punctured spheres, we find a new equality between two symplectic forms defined on it. Namely, by treating the elements of this moduli space as the singular Euclidean metrics on a sphere, we give an interpretation of the complex hyperbolic form, i.e. the K\"ahler form of the complex hyperbolic structure on the moduli space, as a kind of Weil-Petersson form.

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Xiangsheng Wang. 2022-09-22. The complex hyperbolic form as a Weil-Petersson form. https://doi.org/10.1142/s0219199724500068

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