Algebraic dimension of twistor spaces whose fundamental system is a pencil

AbstractIt is shown that there exists a twistor space on the n-fold connected sum of complex projective planes nCP2, whose algebraic dimension is one and whose general fiber of the algebraic reduction is birational to an elliptic ruled surface or a K3 surface. The former kind of twistor spaces are constructed over nCP2 for any n ≥ 5, while the latter kind of example is constructed over 5CP2. Both of these seem to be the first such example on nCP2. The algebraic reduction in these examples is induced by the anti-canonical system of the twistor spaces. It is also shown that the former kind of twistor spaces contain a pair of non-normal Hopf surfaces.

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Thin structure of heterogeneous and multiphase fluid flows

Proceedings of the Mavlyutov Institute of Mechanics ◽

10.21662/uim2012.1.036 ◽

2012 ◽

Vol 9 (1) ◽

pp. 175-180

Author(s):

Yu.D. Chashechkin

Keyword(s):

Large Scale ◽

Fundamental System ◽

Fluid Flows ◽

Regular Solutions ◽

Flow Models ◽

Group Methods ◽

Wide Range ◽

Thin Structure ◽

Multiphase Fluid ◽

Complete Solutions

According to the results of visualization of streams, the existence of structures in a wide range of scales is noted: from galactic to micron. The use of a fundamental system of equations is substantiated based on the results of comparing symmetries of various flow models with the usage of theoretical group methods. Complete solutions of the system are found by the methods of the singular perturbations theory with a condition of compatibility, which determines the characteristic equation. A comparison of complete solutions with experimental data shows that regular solutions characterize large-scale components of the flow, a rich family of singular solutions describes formation of the thin media structure. Examples of calculations and observations of stratified, rotating and multiphase media are given. The requirements for the technique of an adequate experiment are discussed.

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

Proyecciones (Antofagasta) ◽

10.4067/s0716-09172007000300001 ◽

2007 ◽

Vol 26 (3) ◽

Cited By ~ 1

Author(s):

HERMINIA OCHSENIUS ◽

W. H. SCHIKHOF

Keyword(s):

Banach Spaces ◽

Valued Fields ◽

Algebraic Dimension ◽

Arbitrary Rank

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Generalized almost even-Clifford manifolds and their twistor spaces

Complex Manifolds ◽

10.1515/coma-2020-0108 ◽

2021 ◽

Vol 8 (1) ◽

pp. 96-124

Author(s):

Luis Fernando Hernández-Moguel ◽

Rafael Herrera

Keyword(s):

Twistor Space ◽

Complex Structure ◽

Twistor Spaces ◽

Recent Interest ◽

Generalized Complex Structure ◽

Generalized Complex ◽

Space Construction ◽

Clifford Structures

Abstract Motivated by the recent interest in even-Clifford structures and in generalized complex and quaternionic geometries, we introduce the notion of generalized almost even-Clifford structure. We generalize the Arizmendi-Hadfield twistor space construction on even-Clifford manifolds to this setting and show that such a twistor space admits a generalized complex structure under certain conditions.

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Schottky groups acting on homogeneous rational manifolds

Journal für die reine und angewandte Mathematik (Crelles Journal) ◽

10.1515/crelle-2016-0065 ◽

2019 ◽

Vol 2019 (753) ◽

pp. 23-56 ◽

Cited By ~ 1

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.

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