Ampleness of the CM line bundle on the moduli space of canonically polarized varieties

Zsolt Patakfalvi; Chenyang Xu

doi:10.14231/AG-2017-002

Ampleness of the CM line bundle on the moduli space of canonically polarized varieties

Zsolt Patakfalvi, Chenyang Xu

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

11 Scopus citations

Abstract

We prove that the CM line bundle is ample on the proper moduli space which parametrizes KSBA-stable varieties.

Original language	English (US)
Pages (from-to)	29-39
Number of pages	11
Journal	Algebraic Geometry
Volume	4
Issue number	1
DOIs	https://doi.org/10.14231/AG-2017-002
State	Published - Jan 1 2017
Externally published	Yes

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Geometry and Topology

Keywords

Ample
CM line bundle
K-stability
KSBA stable
Moduli space
Stable variety

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10.14231/AG-2017-002

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title = "Ampleness of the CM line bundle on the moduli space of canonically polarized varieties",

abstract = "We prove that the CM line bundle is ample on the proper moduli space which parametrizes KSBA-stable varieties.",

keywords = "Ample, CM line bundle, K-stability, KSBA stable, Moduli space, Stable variety",

author = "Zsolt Patakfalvi and Chenyang Xu",

note = "Publisher Copyright: {\textcopyright} Foundation Compositio Mathematica 2017.",

year = "2017",

month = jan,

day = "1",

doi = "10.14231/AG-2017-002",

language = "English (US)",

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AU - Patakfalvi, Zsolt

AU - Xu, Chenyang

N1 - Publisher Copyright: © Foundation Compositio Mathematica 2017.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - We prove that the CM line bundle is ample on the proper moduli space which parametrizes KSBA-stable varieties.

AB - We prove that the CM line bundle is ample on the proper moduli space which parametrizes KSBA-stable varieties.

KW - Ample

KW - CM line bundle

KW - K-stability

KW - KSBA stable

KW - Moduli space

KW - Stable variety

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JO - Algebraic Geometry

JF - Algebraic Geometry

IS - 1

ER -

Ampleness of the CM line bundle on the moduli space of canonically polarized varieties

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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