Ampleness of canonical divisors of hyperbolic normal projective varieties

Fei Hu; Sheng Meng; De Qi Zhang

doi:10.1007/s00209-014-1351-1

Ampleness of canonical divisors of hyperbolic normal projective varieties

Fei Hu
, Sheng Meng
, De Qi Zhang^*

^*Corresponding author for this work

National University of Singapore

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

8 Scopus citations

Abstract

Let X be a projective variety which is algebraic Lang hyperbolic.We show that Lang conjecture holds one direction only X and all its subvarieties are of general type and the canonical divisor KX is ample at smooth points and Kawamata log terminal points of X provided that KX is Q-Cartier no Calabivariety is algebraic Lang hyperbolic and a weak abundance conjecture holds.

Original language	English
Pages (from-to)	1179-1193
Number of pages	15
Journal	Mathematische Zeitschrift
Volume	278
Issue number	3-4
DOIs	https://doi.org/10.1007/s00209-014-1351-1
State	Published - 12 Nov 2014
Externally published	Yes

Keywords

Algebraic Lang hyperbolic variety
Ample canonical divisor

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10.1007/s00209-014-1351-1

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title = "Ampleness of canonical divisors of hyperbolic normal projective varieties",

abstract = "Let X be a projective variety which is algebraic Lang hyperbolic.We show that Lang conjecture holds one direction only X and all its subvarieties are of general type and the canonical divisor KX is ample at smooth points and Kawamata log terminal points of X provided that KX is Q-Cartier no Calabivariety is algebraic Lang hyperbolic and a weak abundance conjecture holds.",

keywords = "Algebraic Lang hyperbolic variety, Ample canonical divisor",

author = "Fei Hu and Sheng Meng and Zhang, \{De Qi\}",

note = "Publisher Copyright: {\textcopyright} 2014, Springer-Verlag Berlin Heidelberg.",

year = "2014",

month = nov,

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doi = "10.1007/s00209-014-1351-1",

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AU - Hu, Fei

AU - Meng, Sheng

AU - Zhang, De Qi

PY - 2014/11/12

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N2 - Let X be a projective variety which is algebraic Lang hyperbolic.We show that Lang conjecture holds one direction only X and all its subvarieties are of general type and the canonical divisor KX is ample at smooth points and Kawamata log terminal points of X provided that KX is Q-Cartier no Calabivariety is algebraic Lang hyperbolic and a weak abundance conjecture holds.

AB - Let X be a projective variety which is algebraic Lang hyperbolic.We show that Lang conjecture holds one direction only X and all its subvarieties are of general type and the canonical divisor KX is ample at smooth points and Kawamata log terminal points of X provided that KX is Q-Cartier no Calabivariety is algebraic Lang hyperbolic and a weak abundance conjecture holds.

KW - Algebraic Lang hyperbolic variety

KW - Ample canonical divisor

UR - https://www.scopus.com/pages/publications/84911961198

U2 - 10.1007/s00209-014-1351-1

DO - 10.1007/s00209-014-1351-1

M3 - 文章

AN - SCOPUS:84911961198

SN - 0025-5874

VL - 278

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EP - 1193

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3-4

ER -

Ampleness of canonical divisors of hyperbolic normal projective varieties

Abstract

Keywords

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