On a theorem of Campana and Paun

Christian Schnell

On a theorem of Campana and Paun

Christian Schnell

Mathematics

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

4 Scopus citations

Abstract

Let X be a smooth projective variety over the complex numbers, and ∆ ⊆ X a reduced divisor with normal crossings. We present a slightly simplified proof for the following theorem of Campana and Paun: If some tensor power of the bundle Ω¹ _X(log ∆) contains a subsheaf with big determinant, then (X, ∆) is of log general type. This result is a key step in the recent proof of Viehweg's hyperbolicity conjecture.

Original language	English
Article number	8
Journal	Epijournal de Geometrie Algebrique
Volume	1
State	Published - 2017

Keywords

Foliation
Log cotangent bundle
Log general type
Movable curve class
Slope semi-stability
Viehweg's hyperbolicity conjecture

Cite this

@article{d27bdcbea6a84a3485c173ee001786b3,

title = "On a theorem of Campana and Paun",

abstract = "Let X be a smooth projective variety over the complex numbers, and ∆ ⊆ X a reduced divisor with normal crossings. We present a slightly simplified proof for the following theorem of Campana and Paun: If some tensor power of the bundle Ω1 X(log ∆) contains a subsheaf with big determinant, then (X, ∆) is of log general type. This result is a key step in the recent proof of Viehweg's hyperbolicity conjecture.",

keywords = "Foliation, Log cotangent bundle, Log general type, Movable curve class, Slope semi-stability, Viehweg's hyperbolicity conjecture",

author = "Christian Schnell",

note = "Publisher Copyright: {\textcopyright} by the author(s)",

year = "2017",

language = "English",

volume = "1",

journal = "Epijournal de Geometrie Algebrique",

issn = "2491-6765",

}

TY - JOUR

T1 - On a theorem of Campana and Paun

AU - Schnell, Christian

N1 - Publisher Copyright: © by the author(s)

PY - 2017

Y1 - 2017

N2 - Let X be a smooth projective variety over the complex numbers, and ∆ ⊆ X a reduced divisor with normal crossings. We present a slightly simplified proof for the following theorem of Campana and Paun: If some tensor power of the bundle Ω1 X(log ∆) contains a subsheaf with big determinant, then (X, ∆) is of log general type. This result is a key step in the recent proof of Viehweg's hyperbolicity conjecture.

AB - Let X be a smooth projective variety over the complex numbers, and ∆ ⊆ X a reduced divisor with normal crossings. We present a slightly simplified proof for the following theorem of Campana and Paun: If some tensor power of the bundle Ω1 X(log ∆) contains a subsheaf with big determinant, then (X, ∆) is of log general type. This result is a key step in the recent proof of Viehweg's hyperbolicity conjecture.

KW - Foliation

KW - Log cotangent bundle

KW - Log general type

KW - Movable curve class

KW - Slope semi-stability

KW - Viehweg's hyperbolicity conjecture

UR - https://www.scopus.com/pages/publications/85064606798

M3 - Article

AN - SCOPUS:85064606798

SN - 2491-6765

VL - 1

JO - Epijournal de Geometrie Algebrique

JF - Epijournal de Geometrie Algebrique

M1 - 8

ER -

On a theorem of Campana and Paun

Abstract

Keywords

Other files and links

Fingerprint

Cite this