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

Access to Document

10.24033/asens.2365

Cite this

@article{0ba568a1e3cf44e5a3b1d252f2d5e862,

title = "Quasi-projectivity of the moduli space of smooth k{\"a}hler-Einstein fano manifolds",

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",

note = "Publisher Copyright: {\textcopyright} 2018 Soci{\'e}t{\'e} Math{\'e}matique de France. Tous droits r{\'e}serv{\'e}s.",

year = "2018",

month = may,

day = "1",

doi = "10.24033/asens.2365",

language = "English (US)",

volume = "51",

pages = "739--772",

journal = "Annales Scientifiques de l'Ecole Normale Superieure",

issn = "0012-9593",

publisher = "Societe Mathematique de France",

number = "3",

}

TY - JOUR

T1 - Quasi-projectivity of the moduli space of smooth kähler-Einstein fano manifolds

AU - Li, Chi

AU - Wang, Xiaowei

AU - Xu, Chenyang

PY - 2018/5/1

Y1 - 2018/5/1

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.

UR - https://www.scopus.com/pages/publications/85049843332

UR - https://www.scopus.com/inward/citedby.url?scp=85049843332&partnerID=8YFLogxK

U2 - 10.24033/asens.2365

DO - 10.24033/asens.2365

M3 - Article

AN - SCOPUS:85049843332

SN - 0012-9593

VL - 51

SP - 739

EP - 772

JO - Annales Scientifiques de l'Ecole Normale Superieure

JF - Annales Scientifiques de l'Ecole Normale Superieure

IS - 3

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this