On the universal coverings of algebraic surfaces

L. Katzarkov; M. Ramachandran

doi:10.1016/S0012-9593(98)80105-5

On the universal coverings of algebraic surfaces

L. Katzarkov
, M. Ramachandran

Mathematics

University of California at Irvine

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

18 Scopus citations

Abstract

In this paper we use some recent developments in Nonabelian Hodge theory to study the existence of holomorphic functions on the universal coverings of algebraic surfaces. In particular we prove that if the fundamental group of an algebraic surface is reductive then its universal covering is holomorphically convex. This is a partial verification of the Shafarevich conjecture claiming that the universal covering of a smooth projective variety is holomorphically convex.

Original language	English
Pages (from-to)	525-535
Number of pages	11
Journal	Annales Scientifiques de l'Ecole Normale Superieure
Volume	31
Issue number	4
DOIs	https://doi.org/10.1016/S0012-9593(98)80105-5
State	Published - 1998

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title = "On the universal coverings of algebraic surfaces",

abstract = "In this paper we use some recent developments in Nonabelian Hodge theory to study the existence of holomorphic functions on the universal coverings of algebraic surfaces. In particular we prove that if the fundamental group of an algebraic surface is reductive then its universal covering is holomorphically convex. This is a partial verification of the Shafarevich conjecture claiming that the universal covering of a smooth projective variety is holomorphically convex.",

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AB - In this paper we use some recent developments in Nonabelian Hodge theory to study the existence of holomorphic functions on the universal coverings of algebraic surfaces. In particular we prove that if the fundamental group of an algebraic surface is reductive then its universal covering is holomorphically convex. This is a partial verification of the Shafarevich conjecture claiming that the universal covering of a smooth projective variety is holomorphically convex.

UR - https://www.scopus.com/pages/publications/0032114289

U2 - 10.1016/S0012-9593(98)80105-5

DO - 10.1016/S0012-9593(98)80105-5

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SN - 0012-9593

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JO - Annales Scientifiques de l'Ecole Normale Superieure

JF - Annales Scientifiques de l'Ecole Normale Superieure

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On the universal coverings of algebraic surfaces

Abstract

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