The fundamental group of a toroidal compactification of a Hermitian locally symmetric space

2013/06/01 by Kasparian, Azniv
#14M27 #32M12 #53C35 #55Q52 #57T15 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1306.0126

Abstract

The present work obtains the fundamental group of a toroidal compactification X' of a non-compact quotient X of a Hermitian symmetric space D of non-compact type by a lattice L in the isometry group G of D. As a consequence it derives the equality of the ranks of the first homology groups of X' and X with integral coefficients. The paper provides also a sufficient condition on a torsion free non-uniform lattice L, under which the fundamental group of X' is residually finite. Articles of Hummel-Schroeder, Hummel and Di Cerbo imply that the toroidal compactifications X' of generic non-compact torsion free quotients X of the complex balls satisfy this sufficient condition.

Related

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• Compactification de Chabauty des espaces symétriques de type non compact
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• Boundary branch divisor of toroidal compactifications