On the continuity of Weil-Petersson volumes of the moduli space weighted points on the projective line

Salvatore Tambasco

doi:10.1515/coma-2021-0137

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arXiv · 2109.05007

On the continuity of Weil-Petersson volumes of the moduli space weighted points on the projective line

Salvatore Tambasco

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Abstract

In this work we show that the Weil-Petersson volume (which coincides with the CM degree) in the case of weighted points in the projective line is continuous when approaching the Calabi-Yau geometry from the Fano geometry. More specifically, the CM volume computed via localization converges to the geometric volume, computed by McMullen with different techniques, when the sum of the weights approaches the Calabi-Yau geometry.

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BibTeX RIS

Salvatore Tambasco. 2024-02-06. On the continuity of Weil-Petersson volumes of the moduli space weighted points on the projective line. https://doi.org/10.1515/coma-2021-0137

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