Twistor examples of algebraic dimension zero threefolds

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

scholarly journals Affine Connections on Complex Manifolds of Algebraic Dimension Zero

2016 ◽  
Vol 16 (4) ◽  
pp. 675-689
Author(s):  
Sorin Dumitrescu ◽  
Benjamin McKay
Keyword(s):  
Complex Manifolds ◽  
Affine Connections ◽  
Algebraic Dimension ◽  
Dimension Zero

scholarly journals CARTAN GEOMETRIES ON COMPLEX MANIFOLDS OF ALGEBRAIC DIMENSION ZERO

2019 ◽  
Vol Volume 3 ◽  
Author(s):  
Indranil Biswas ◽  
Sorin Dumitrescu ◽  
Benjamin McKay
Keyword(s):  
Complex Manifolds ◽  
Cartan Geometry ◽  
Algebraic Dimension ◽  
Dimension Zero ◽  
Special Cases ◽  
Nous Montrons ◽  
Cartan Geometries ◽  
International Audience ◽  
Holomorphic Affine ◽  
Compact Complex Manifolds

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.

scholarly journals ON THE ALGEBRAIC DIMENSION OF BANACH SPACES OVER NON-ARCHIMEDEAN VALUED FIELDS OR ARBITRARY RANK

2007 ◽  
Vol 26 (3) ◽  
Author(s):  
HERMINIA OCHSENIUS ◽  
W. H. SCHIKHOF
Keyword(s):  
Banach Spaces ◽  
Valued Fields ◽  
Algebraic Dimension ◽  
Arbitrary Rank

scholarly journals Schottky groups acting on homogeneous rational manifolds

2019 ◽  
Vol 2019 (753) ◽  
pp. 23-56 ◽  
Author(s):  
Christian Miebach ◽  
Karl Oeljeklaus
Keyword(s):  
Deformation Theory ◽  
Group Actions ◽  
Picard Group ◽  
Schottky Group ◽  
Fundamental Groups ◽  
Complex Manifolds ◽  
Schottky Groups ◽  
Algebraic Dimension ◽  
Geometric Invariants ◽  
Compact Complex Manifolds

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.

scholarly journals On approximate triangular decompositions in dimension zero

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

Free quotients of infinite rank of GL2 over Dedekind domains

1999 ◽  
Vol 129 (1) ◽  
pp. 77-84
Author(s):  
A. W. Mason
Keyword(s):  
Factor Group ◽  
Krull Dimension ◽  
Two Dimensional ◽  
Integral Domains ◽  
Dimension Zero ◽  
Infinite Rank ◽  
Dedekind Domains ◽  
Free Quotient

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.

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