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

IF 0.5 Q3 MATHEMATICS

Complex Manifolds Pub Date : 2021-09-10 DOI:10.1515/coma-2021-0137

Salvatore Tambasco

引用次数: 0

Abstract

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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投影线上模空间加权点的Weil-Petersson体积的连续性

在这项工作中，我们证明了在投影线上加权点的情况下，当从Fano几何接近Calabi-Yau几何时，Weil-Petersson体积(与CM度一致)是连续的。更具体地说，当权重和接近Calabi-Yau几何形状时，通过定位计算的CM体积收敛于McMullen用不同技术计算的几何体积。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Complex Manifolds MATHEMATICS-

CiteScore

1.30

自引率

20.00%

发文量

审稿时长

25 weeks

期刊介绍： Complex Manifolds is devoted to the publication of results on these and related topics: Hermitian geometry, Kähler and hyperkähler geometry Calabi-Yau metrics, PDE''s on complex manifolds Generalized complex geometry Deformations of complex structures Twistor theory Geometric flows on complex manifolds Almost complex geometry Quaternionic geometry Geometric theory of analytic functions Holomorphic dynamics Several complex variables Dolbeault cohomology CR geometry.