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

Chi Li; Xiaowei Wang; Chenyang Xu

doi:10.24033/asens.2365

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

Chi Li, Xiaowei Wang, Chenyang Xu

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

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

Original language	English (US)
Pages (from-to)	739-772
Number of pages	34
Journal	Annales Scientifiques de l'Ecole Normale Superieure
Volume	51
Issue number	3
DOIs	https://doi.org/10.24033/asens.2365
State	Published - May 1 2018
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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abstract = "In this paper, we prove that there is a canonical continuous Hermitian metric on the CM line bundle over the proper moduli space M of smoothable K{\"a}hler-Einstein Fano varieties. The Chern curvature of this Hermitian metric is the Weil-Petersson current, which exists as a closed positive (1,1)-current on M and extends the canonical Weil-Petersson current on the moduli space M of smooth K{\"a}hler-Einstein Fano manifolds. As a consequence, we show that the CM line bundle is nef and big on M and its restriction on M is ample.",

author = "Chi Li and Xiaowei Wang and Chenyang Xu",

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AU - Li, Chi

AU - Wang, Xiaowei

AU - Xu, Chenyang

PY - 2018/5/1

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N2 - In this paper, we prove that there is a canonical continuous Hermitian metric on the CM line bundle over the proper moduli space M of smoothable Kähler-Einstein Fano varieties. The Chern curvature of this Hermitian metric is the Weil-Petersson current, which exists as a closed positive (1,1)-current on M and extends the canonical Weil-Petersson current on the moduli space M of smooth Kähler-Einstein Fano manifolds. As a consequence, we show that the CM line bundle is nef and big on M and its restriction on M is ample.

AB - In this paper, we prove that there is a canonical continuous Hermitian metric on the CM line bundle over the proper moduli space M of smoothable Kähler-Einstein Fano varieties. The Chern curvature of this Hermitian metric is the Weil-Petersson current, which exists as a closed positive (1,1)-current on M and extends the canonical Weil-Petersson current on the moduli space M of smooth Kähler-Einstein Fano manifolds. 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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Quasi-projectivity of the moduli space of smooth kähler-Einstein fano manifolds

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