Compact quotients of large domains in complex projective space

Finnur Lárusson

Annales de l'institut Fourier (1998)

  • Volume: 48, Issue: 1, page 223-246
  • ISSN: 0373-0956

Abstract

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We study compact complex manifolds covered by a domain in n -dimensional projective space whose complement E is non-empty with ( 2 n - 2 ) -dimensional Hausdorff measure zero. Such manifolds only exist for n ≥ 3 . They do not belong to the class 𝒞 , so they are neither Kähler nor Moishezon, their Kodaira dimension is - ∞ , their fundamental groups are generalized Kleinian groups, and they are rationally chain connected. We also consider the two main classes of known 3-dimensional examples: Blanchard manifolds, for which E is a line, and the generalized Schottky coverings constructed by Nori. We determine their function fields and describe the surfaces they contain.

How to cite

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Lárusson, Finnur. "Compact quotients of large domains in complex projective space." Annales de l'institut Fourier 48.1 (1998): 223-246. <http://eudml.org/doc/75277>.

@article{Lárusson1998,
abstract = {We study compact complex manifolds covered by a domain in $n$-dimensional projective space whose complement $E$ is non-empty with $(2n-2)$-dimensional Hausdorff measure zero. Such manifolds only exist for $n\ge 3$. They do not belong to the class $\{\cal C\}$, so they are neither Kähler nor Moishezon, their Kodaira dimension is $-\infty $, their fundamental groups are generalized Kleinian groups, and they are rationally chain connected. We also consider the two main classes of known 3-dimensional examples: Blanchard manifolds, for which $E$ is a line, and the generalized Schottky coverings constructed by Nori. We determine their function fields and describe the surfaces they contain.},
author = {Lárusson, Finnur},
journal = {Annales de l'institut Fourier},
keywords = {compact quotients; covering space; Schottky coverings; Blanchard manifolds; Kato manifolds},
language = {eng},
number = {1},
pages = {223-246},
publisher = {Association des Annales de l'Institut Fourier},
title = {Compact quotients of large domains in complex projective space},
url = {http://eudml.org/doc/75277},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Lárusson, Finnur
TI - Compact quotients of large domains in complex projective space
JO - Annales de l'institut Fourier
PY - 1998
PB - Association des Annales de l'Institut Fourier
VL - 48
IS - 1
SP - 223
EP - 246
AB - We study compact complex manifolds covered by a domain in $n$-dimensional projective space whose complement $E$ is non-empty with $(2n-2)$-dimensional Hausdorff measure zero. Such manifolds only exist for $n\ge 3$. They do not belong to the class ${\cal C}$, so they are neither Kähler nor Moishezon, their Kodaira dimension is $-\infty $, their fundamental groups are generalized Kleinian groups, and they are rationally chain connected. We also consider the two main classes of known 3-dimensional examples: Blanchard manifolds, for which $E$ is a line, and the generalized Schottky coverings constructed by Nori. We determine their function fields and describe the surfaces they contain.
LA - eng
KW - compact quotients; covering space; Schottky coverings; Blanchard manifolds; Kato manifolds
UR - http://eudml.org/doc/75277
ER -

References

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