Fibrations of compact Kähler manifolds in terms of cohomological properties of their fundamental groups

Mok, Ngaiming. "Fibrations of compact Kähler manifolds in terms of cohomological properties of their fundamental groups." Annales de l'institut Fourier 50.2 (2000): 633-675. <http://eudml.org/doc/75431>.

@article{Mok2000,
abstract = {We prove fibration theorems on compact Kähler manifolds with conditions on first cohomology groups of fundamental groups with respect to unitary representations into Hilbert spaces. If the fundamental group T of compact Kähler manifold X violates Property (T) of Kazhdan’s, then $H^1(Gamma ,\Phi )\ne 0$ for some unitary representation $\Phi $. By our earlier work there exists a $d$-closed holomorphic 1-form with coefficients twisted by some unitary representation $\Phi ^\{\prime \}$, possibly non-isomorphic to $\Phi $. Taking norms we obtains a positive semi-definite $d$-closed $(1,1)$-form $\nu $ sur $x$, which underlies a semi-Khäler structure. We study meromorphic foliations related to this semi-Khäler structure and another semi-Khäler structure related to the Ricci form to prove fibration theorems on some modification of an unramified finite cover of $x$. The base manifold is shown to be either a compact complex torus or a variety of logarithmic general type with respect to the multiplicity locus of the holomorphic fibration.},
author = {Mok, Ngaiming},
journal = {Annales de l'institut Fourier},
keywords = {compact Kähler manifolds; holomorphic fibration; foliation; harmonic maps and forms},
language = {eng},
number = {2},
pages = {633-675},
publisher = {Association des Annales de l'Institut Fourier},
title = {Fibrations of compact Kähler manifolds in terms of cohomological properties of their fundamental groups},
url = {http://eudml.org/doc/75431},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Mok, Ngaiming
TI - Fibrations of compact Kähler manifolds in terms of cohomological properties of their fundamental groups
JO - Annales de l'institut Fourier
PY - 2000
PB - Association des Annales de l'Institut Fourier
VL - 50
IS - 2
SP - 633
EP - 675
AB - We prove fibration theorems on compact Kähler manifolds with conditions on first cohomology groups of fundamental groups with respect to unitary representations into Hilbert spaces. If the fundamental group T of compact Kähler manifold X violates Property (T) of Kazhdan’s, then $H^1(Gamma ,\Phi )\ne 0$ for some unitary representation $\Phi $. By our earlier work there exists a $d$-closed holomorphic 1-form with coefficients twisted by some unitary representation $\Phi ^{\prime }$, possibly non-isomorphic to $\Phi $. Taking norms we obtains a positive semi-definite $d$-closed $(1,1)$-form $\nu $ sur $x$, which underlies a semi-Khäler structure. We study meromorphic foliations related to this semi-Khäler structure and another semi-Khäler structure related to the Ricci form to prove fibration theorems on some modification of an unramified finite cover of $x$. The base manifold is shown to be either a compact complex torus or a variety of logarithmic general type with respect to the multiplicity locus of the holomorphic fibration.
LA - eng
KW - compact Kähler manifolds; holomorphic fibration; foliation; harmonic maps and forms
UR - http://eudml.org/doc/75431
ER -