PREFACE xi
There are two appendices summarising standard material used throughout the
book. The first appendix, written by J.A. and D.K., presents some generalities
about projective completions of finitely generated groups, and the second one serves
as a reference for results in Hodge theory.
The main topic not covered in this book is the so-called Shafarevich
conjecture3.
At the end of his book [114], Shafarevich raised the question whether the universal
covering of a smooth complex algebraic variety has to be holomorphically convex,
and one can ask the same question for arbitrary compact Kahler manifolds. Over
the last few years, the question of Shafarevich has led to intense activities in al-
gebraic geometry. These are obviously related to the study of Kahler groups, but
they tend to have a different flavour from the material presented in this book. We
refer the reader to the recent monograph by Kollar [81] for an overview of this
topic. See also [13], [79].
The 1995 Borel Seminar was organised by D. Kotschick and M. Burger with the
cooperation of N. A'Campo and J. Amoros. It met ten times for a total of twenty-
five lectures given by N. A'Campo, J. Amoros, M. Burger, F. Campana, J. Carl-
son, K. Corlette, D. Kotschick, F. Labourie, S. Maier, D. Toledo, A. Valette and
K. Zuo. The lecturers at a preparatory meeting in December 1994 were F. Catanese
and D. Kotschick. Financial support was provided by the Hie Cycle Romand de
Mathematiques, the Swiss National Fund and the University of Basle.
We are grateful to all the speakers, and to the other participants, for their
valuable contributions to the seminar, and, by extension, to our understanding of
the topic of this book.
J.A, M.B., K.C., D.K. and D.T.
December 1995
Authors' addresses:
J.A.:
DEPARTAMENT DE MATEMATICA APLICADA
I, ETSEIB,
UNIVERSITAT
POLITECNICA DE CATALUNYA, A V . DIAGONAL 6 4 7 , 0 8 0 2 8 BARCELONA, SPAIN
M.B.: INSTITUT DE MATHEMATIQUES, UNIVERSITE DE LAUSANNE, 101 5 LAU-
SANNE, S W I T Z E R L A N D
K.C.:
DEPARTMENT OF MATHEMATICS, UNIVERSITY OF CHICAGO,
5734
SOUTH
UNIVERSITY AVENUE, CHICAGO, ILLINOIS
60637, U.S.A.
D.K.: MATHEMATISCHES INSTITUT, UNIVERSITAT BASEL, RHEINSPRUNG 21,
4051 BASEL, SWITZERLAND
D.T.: DEPARTMENT OF MATHEMATICS, UNIVERSITY OF UTAH, SALT LAKE CITY,
UTAH 84112, U.S.A.
In the seminar this was discussed in lectures of F. Campana and K. Zuo.
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