Twistor examples of algebraic dimension zero threefolds

1991 ◽  
Vol 103 (1) ◽  
pp. 537-545 ◽  
Author(s):  
M. Ville

2016 ◽  
Vol 16 (4) ◽  
pp. 675-689
Author(s):  
Sorin Dumitrescu ◽  
Benjamin McKay


2019 ◽  
Vol Volume 3 ◽  
Author(s):  
Indranil Biswas ◽  
Sorin Dumitrescu ◽  
Benjamin McKay

International audience We show that compact complex manifolds of algebraic dimension zero bearing a holomorphic Cartan geometry of algebraic type have infinite fundamental group. This generalizes the main Theorem in [DM] where the same result was proved for the special cases of holomorphic affine connections and holomorphic conformal structures. Nous montrons que toute variété complexe compacte de dimension algébrique nulle possédant une géométrie de Cartan holomorphe de type algébrique doit avoir un groupe fondamental infini. Il s’agit d’une généralisation du théorème principal de [DM] où le même résultat était montré dans le cas particulier des connexions affines holomorphes et des structures conformes holomorphes.





2019 ◽  
Vol 2019 (753) ◽  
pp. 23-56 ◽  
Author(s):  
Christian Miebach ◽  
Karl Oeljeklaus

AbstractWe systematically study Schottky group actions on homogeneous rational manifolds and find two new families besides those given by Nori’s well-known construction. This yields new examples of non-Kähler compact complex manifolds having free fundamental groups. We then investigate their analytic and geometric invariants such as the Kodaira and algebraic dimension, the Picard group and the deformation theory, thus extending results due to Lárusson and to Seade and Verjovsky. As a byproduct, we see that the Schottky construction allows to recover examples of equivariant compactifications of {{\rm{SL}}(2,\mathbb{C})/\Gamma} for Γ a discrete free loxodromic subgroup of {{\rm{SL}}(2,\mathbb{C})}, previously obtained by A. Guillot.



2007 ◽  
Vol 42 (7) ◽  
pp. 693-716 ◽  
Author(s):  
Marc Moreno Maza ◽  
Greg Reid ◽  
Robin Scott ◽  
Wenyuan Wu
Keyword(s):  


Author(s):  
A. W. Mason

This paper is concerned with integral domains R, for which the factor group SL2(R)/U2(R) has a non-trivial, free quotient, where U2(R) is the subgroup of GL2(R) generated by the unipotent matrices. Recently, Krstić and McCool have proved that SL2(P[x])/U2(P[x]) has a free quotient of infinite rank, where P is a domain which is not a field. This extends earlier results of Grunewald, Mennicke and Vaserstein.Any ring of the type P[x] has Krull dimension at least 2. The purpose of this paper is to show that result of Krstić and McCool extends to some domains of Krull dimension 1, in particular to certain Dedekind domains. This result, which represents a two-dimensional anomaly is the best possible in the following sense. It is well known that SL2(R) = U2(R), when R is a domain of Krull dimension zero, i.e. when R is a field. It is already known that for some arithmetic Dedekind domains A, the factor group SL2(A)/U2(A) has a free quotient of finite (and not infinite) rank.



Sign in / Sign up

Export Citation Format

Share Document