Algebraic varieties with quasi-projective universal cover

Benoît Claudon; Andreas Höring; János Kollár

doi:10.1515/crelle.2012.017

Algebraic varieties with quasi-projective universal cover

Benoît Claudon
, Andreas Höring
, János Kollár

Mathematics

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

4 Scopus citations

Abstract

We prove that the universal cover of a normal projective variety X is quasi-projective iff a finite étale cover of X is a fiber bundle over an Abelian variety with simply connected fiber.

Original language	English (US)
Pages (from-to)	207-221
Number of pages	15
Journal	Journal fur die Reine und Angewandte Mathematik
Issue number	679
DOIs	https://doi.org/10.1515/crelle.2012.017
State	Published - Jun 2013

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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title = "Algebraic varieties with quasi-projective universal cover",

abstract = "We prove that the universal cover of a normal projective variety X is quasi-projective iff a finite {\'e}tale cover of X is a fiber bundle over an Abelian variety with simply connected fiber.",

author = "Beno{\^i}t Claudon and Andreas H{\"o}ring and J{\'a}nos Koll{\'a}r",

note = "Funding Information: Acknowledgement. The authors want to thank D. Greb, T. Peternell and C. Voisin for useful comments and references. B.C. and A.H. were partially supported by the A.N.R. project {\textquoteleft}{\textquoteleft}CLASS{\textquoteright}{\textquoteright}. The paper was written while A.H. enjoyed the hospitality of the Albert-Ludwigs-Universit{\"a}t in Freiburg. Partial financial support for J.K. was provided by the NSF under grant number DMS-0758275.",

year = "2013",

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doi = "10.1515/crelle.2012.017",

language = "English (US)",

pages = "207--221",

journal = "Journal fur die Reine und Angewandte Mathematik",

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AU - Claudon, Benoît

AU - Höring, Andreas

AU - Kollár, János

N1 - Funding Information: Acknowledgement. The authors want to thank D. Greb, T. Peternell and C. Voisin for useful comments and references. B.C. and A.H. were partially supported by the A.N.R. project ‘‘CLASS’’. The paper was written while A.H. enjoyed the hospitality of the Albert-Ludwigs-Universität in Freiburg. Partial financial support for J.K. was provided by the NSF under grant number DMS-0758275.

PY - 2013/6

Y1 - 2013/6

N2 - We prove that the universal cover of a normal projective variety X is quasi-projective iff a finite étale cover of X is a fiber bundle over an Abelian variety with simply connected fiber.

AB - We prove that the universal cover of a normal projective variety X is quasi-projective iff a finite étale cover of X is a fiber bundle over an Abelian variety with simply connected fiber.

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UR - https://www.scopus.com/pages/publications/84881527091#tab=citedBy

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DO - 10.1515/crelle.2012.017

M3 - Article

AN - SCOPUS:84881527091

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SP - 207

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JO - Journal fur die Reine und Angewandte Mathematik

JF - Journal fur die Reine und Angewandte Mathematik

IS - 679

ER -

Algebraic varieties with quasi-projective universal cover

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