Quasi-projectivity of the moduli space of smooth kähler-Einstein fano manifolds

IF 1.3 1区数学 Q1 MATHEMATICS

Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2018-05-01 DOI:10.24033/ASENS.2365

Chi Li, Chi Li, Xiaowei Wang, Chenyang Xu

引用次数: 4

Abstract

In this note, we prove that there is a canonical continuous Hermitian metric on the CM line bundle over the proper moduli space M of smoothable Kahler-Einstein Fano varieties. The curvature of this metric is the Weil-Petersson current, which exists as a positive (1,1)-current on M and extends the canonical Weil-Petersson current on the moduli space parametrizing smooth Kahler-Einstein Fano manifoldsM. As a consequence, we show that the CM line bundle is nef and big on M and its restriction on M is ample.

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光滑kähler-Einstein范诺流形模空间的拟投影性

在本文中，我们证明了在光滑Kahler-Einstein Fano变体的固有模空间M上CM线束上存在一个正则连续厄米度规。这个度规的曲率是Weil-Petersson电流，它在M上以正(1,1)电流的形式存在，并在模空间参数化光滑Kahler-Einstein范诺流形sm上扩展了规范Weil-Petersson电流。因此，我们证明了CM线束在M上是nef和大的，并且它对M的限制是充分的。

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

Annales Scientifiques De L Ecole Normale Superieure 数学-数学

CiteScore

3.00

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Annales scientifiques de l''École normale supérieure were founded in 1864 by Louis Pasteur. The journal dealt with subjects touching on Physics, Chemistry and Natural Sciences. Around the turn of the century, it was decided that the journal should be devoted to Mathematics. Today, the Annales are open to all fields of mathematics. The Editorial Board, with the help of referees, selects articles which are mathematically very substantial. The Journal insists on maintaining a tradition of clarity and rigour in the exposition. The Annales scientifiques de l''École normale supérieures have been published by Gauthier-Villars unto 1997, then by Elsevier from 1999 to 2007. Since January 2008, they are published by the Société Mathématique de France.