Hyperbolicity properties of quotient surfaces by freely operating arithmetic lattices
type: Item
instance of: scholarly article
title: Hyperbolicity properties of quotient surfaces by freely operating arithmetic lattices
zbMATH Open document ID: 0952.32015
author: Eberhard Oeljeklaus
author: Christina Schmerling
publication date: 2000-03-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75412
review text: The authors are dealing with hyperbolicity properties of quotient surfaces. They prove the following theorem: Let \(D\) be a symmetric domain in \(\mathbb{C}^2\) and \(\Gamma\subset \Aut^0D\) an irreducible arithmetic lattice which operates freely on \(D\). Then the cusp-compactification \(\overline X\) of \(X= D/\Gamma\) is hyperbolic (cusp-compactification in the sense of Baily-Borel). As a corollary they obtain the following: The minimal resolution of the singularities of \(\overline X,\widehat X@>\pi>>\overline X\) is of general type and hyperbolic \(\text{mod }R\), \(R= \pi^{-1}(\overline X\setminus X)\), i.e., if \(d_{\widehat X}\) is the Kobayashi pseudometric on \(\widehat X\), \(d_{\widehat X}(x,y)= 0\) implies \(x= y\) or that \(x,y\in R\).
Mathematics Subject Classification ID: 32M15
Mathematics Subject Classification ID: 32J15
Mathematics Subject Classification ID: 32S45
Mathematics Subject Classification ID: 32Q45
Mathematics Subject Classification ID: 32N15
Mathematics Subject Classification ID: 32F45
zbMATH DE Number: 1409068
zbMATH Keywords: hyperbolicity
zbMATH Keywords: quotient surfaces
reviewed by: Giuseppe Tomassini
MaRDI profile type: Publication
OpenAlex ID: W2098394610
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DOI: 10.5802/AIF.1751
published in: Annales de l’institut Fourier
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description: scientific article; zbMATH DE number 1409068