scholarly journals Dolbeault cohomology of nilmanifolds with left-invariant complex structure

2011 ◽  
pp. 369-392 ◽  
Author(s):  
Sönke Rollenske
Keyword(s):  
Complex Structure ◽  
Dolbeault Cohomology ◽  
Invariant Complex Structure

scholarly journals TWISTING OF N=1 SUSY GAUGE THEORIES AND HETEROTIC TOPOLOGICAL THEORIES

1995 ◽  
Vol 10 (30) ◽  
pp. 4325-4357 ◽  
Author(s):  
A. JOHANSEN
Keyword(s):  
Complex Structure ◽  
Kähler Manifold ◽  
Dolbeault Cohomology ◽  
Kähler Metric ◽  
Yang Mills ◽  
Kahler Manifold ◽  
Brst Charge ◽  
Kahler Metric ◽  
Compact Kähler Manifold ◽  
Topological Theories

It is shown that D=4N=1 SUSY Yang-Mills theory with an appropriate supermultiplet of matter can be twisted on a compact Kähler manifold. The conditions for cancellation of anomalies of BRST charge are found. The twisted theory has an appropriate BRST charge. We find a nontrivial set of physical operators defined as classes of the cohomology of this BRST operator. We prove that the physical correlators are independent of the external Kähler metric up to a power of a ratio of two Ray-Singer torsions for the Dolbeault cohomology complex on a Kähler manifold. The correlators of local physical operators turn out to be independent of antiholomorphic coordinates defined with a complex structure on the Kähler manifold. However, a dependence of the correlators on holomorphic coordinates can still remain. For a hyper-Kähler metric the physical correlators turn out to be independent of all coordinates of insertions of local physical operators.

scholarly journals On the Bott–Chern cohomology and balanced Hermitian nilmanifolds

2014 ◽  
Vol 25 (06) ◽  
pp. 1450057 ◽  
Author(s):  
Adela Latorre ◽  
Luis Ugarte ◽  
Raquel Villacampa
Keyword(s):  
Cohomology Group ◽  
Complex Structure ◽  
Hermitian Metrics ◽  
Invariant Complex Structure

The Bott–Chern cohomology of six-dimensional nilmanifolds endowed with invariant complex structure is studied with special attention to the cases when balanced or strongly Gauduchon Hermitian metrics exist. We consider complex invariants introduced by Angella and Tomassini and by Schweitzer, which are related to the [Formula: see text]-lemma condition and defined in terms of the Bott–Chern cohomology, and show that the vanishing of some of these invariants is not a closed property under holomorphic deformations. In the balanced case, we determine the spaces that parametrize deformations in type IIB supergravity described by Tseng and Yau in terms of the Bott–Chern cohomology group of bidegree (2, 2).

scholarly journals STABILITY OF ABELIAN COMPLEX STRUCTURES

2006 ◽  
Vol 17 (04) ◽  
pp. 401-416 ◽  
Author(s):  
S. CONSOLE ◽  
A. FINO ◽  
Y. S. POON
Keyword(s):  
Deformation Process ◽  
Complex Structure ◽  
Complex Structures ◽  
Higher Dimension ◽  
Real Dimension ◽  
Small Deformations ◽  
Invariant Complex Structure

Let M = Γ\G be a nilmanifold endowed with an invariant complex structure. We prove that Kuranishi deformations of abelian complex structures are all invariant complex structures, generalizing a result in [7] for 2-step nilmanifolds. We characterize small deformations that remain abelian. As an application, we observe that at real dimension six, the deformation process of abelian complex structures is stable within the class of nilpotent complex structures. We give an example to show that this property does not hold in higher dimension.

On the Kobayashi Pseudometric Reduction of Homogeneous Spaces

1988 ◽  
Vol 31 (1) ◽  
pp. 45-51 ◽  
Author(s):  
Bruce Gilligan
Keyword(s):  
Bounded Domain ◽  
Complex Manifold ◽  
Homogeneous Spaces ◽  
Complex Structure ◽  
Complex Submanifold ◽  
Technical Assumption ◽  
Homogeneous Complex ◽  
Homogeneous Complex Manifold ◽  
Kobayashi Pseudometric ◽  
Invariant Complex Structure

AbstractGiven any homogeneous complex manifold X = G/H, there exists a natural coset map π :G/H → G/K satisfying π (X1) = π (x2) if and only if dx(x1 x2) = 0, where dx denotes the Kobayashi pseudometric on X. Its typical fiber Z : = K/H is a connected complex submanifold of X. Also G/K has a (7-invariant complex structure, provided K satisfies a certain technical assumption (see Theorem 3). If Z is compact as well, then G/K is biholomorphic to a homogeneous bounded domain.

scholarly journals Holomorphic Poisson Cohomology

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Zhuo Chen ◽  
Daniele Grandini ◽  
Yat-Sun Poon
Keyword(s):  
Spectral Sequence ◽  
Complex Structure ◽  
Complex Structures ◽  
Dolbeault Cohomology ◽  
Double Complex ◽  
Poisson Cohomology ◽  
Compact Complex Surfaces ◽  
Generalized Geometry ◽  
Holomorphic Poisson Cohomology ◽  
Compact Complex Manifolds

AbstractHolomorphic Poisson structures arise naturally in the realm of generalized geometry. A holomorphic Poisson structure induces a deformation of the complex structure in a generalized sense, whose cohomology is obtained by twisting the Dolbeault @-operator by the holomorphic Poisson bivector field. Therefore, the cohomology space naturally appears as the limit of a spectral sequence of a double complex. The first sheet of this spectral sequence is simply the Dolbeault cohomology with coefficients in the exterior algebra of the holomorphic tangent bundle. We identify various necessary conditions on compact complex manifolds on which this spectral sequence degenerates on the level of the second sheet. The manifolds to our concern include all compact complex surfaces, Kähler manifolds, and nilmanifolds with abelian complex structures or parallelizable complex structures.

scholarly journals Some relations between Hodge numbers and invariant complex structures on compact nilmanifolds

2017 ◽  
Vol 4 (1) ◽  
pp. 73-83
Author(s):  
Takumi Yamada
Keyword(s):  
Lie Algebra ◽  
Lie Group ◽  
Complex Structure ◽  
Complex Structures ◽  
Nilpotent Lie Group ◽  
Hodge Numbers ◽  
Compact Nilmanifolds ◽  
Simply Connected ◽  
Invariant Complex Structure

AbstractLet N be a simply connected real nilpotent Lie group, n its Lie algebra, and € a lattice in N. If a left-invariant complex structure on N is Γ-rational, then HƏ̄s,t(Γ/N) ≃ HƏ̄s,t(nC) for each s; t. We can construct different left-invariant complex structures on one nilpotent Lie group by using the complexification and the scalar restriction. We investigate relationships to Hodge numbers of associated compact complex nilmanifolds.

COMPLEX STRUCTURES ON FOUR-MANIFOLDS WITH SYMPLECTIC TWO-TORUS ACTIONS

2011 ◽  
Vol 22 (03) ◽  
pp. 449-463 ◽  
Author(s):  
J. J. DUISTERMAAT ◽  
A. PELAYO
Keyword(s):  
General Theory ◽  
Complex Structure ◽  
Torus Action ◽  
K3 Surface ◽  
Complex Structures ◽  
Complex Surfaces ◽  
Torus Actions ◽  
Kähler Structure ◽  
Four Manifolds ◽  
Invariant Complex Structure

We apply the general theory for symplectic torus actions with symplectic or coisotropic orbits to prove that a four-manifold with a symplectic two-torus action admits an invariant complex structure and give an identification of those that do not admit a Kähler structure with Kodaira's class of complex surfaces which admit a nowhere vanishing holomorphic (2,0)-form, but are not a torus nor a K3 surface.

scholarly journals A Hodge-type decomposition of holomorphic Poisson cohomology on nilmanifolds

2017 ◽  
Vol 4 (1) ◽  
pp. 137-154 ◽  
Author(s):  
Yat Sun Poon ◽  
John Simanyi
Keyword(s):  
Spectral Sequence ◽  
Complex Structure ◽  
Adjoint Action ◽  
Poisson Structures ◽  
Dolbeault Cohomology ◽  
Poisson Cohomology ◽  
Abelian Complex Structure ◽  
Nijenhuis Bracket ◽  
Holomorphic Poisson Cohomology ◽  
Type Decomposition

Abstract A cohomology theory associated to a holomorphic Poisson structure is the hypercohomology of a bicomplex where one of the two operators is the classical მ̄-operator, while the other operator is the adjoint action of the Poisson bivector with respect to the Schouten-Nijenhuis bracket. The first page of the associated spectral sequence is the Dolbeault cohomology with coefficients in the sheaf of germs of holomorphic polyvector fields. In this note, the authors investigate the conditions for which this spectral sequence degenerates on the first page when the underlying complex manifolds are nilmanifolds with an abelian complex structure. For a particular class of holomorphic Poisson structures, this result leads to a Hodge-type decomposition of the holomorphic Poisson cohomology. We provide examples when the nilmanifolds are 2-step.

A new method of complex structure analysis by electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 628-629
Author(s):  
V.V. Rybin ◽  
E.V. Voronina
Keyword(s):  
Complex Structure ◽  
Reciprocal Lattice ◽  
Stacking Faults ◽  
Plastic Strains ◽  
Base Position ◽  
Structural Regularity ◽  
Orientation Matrix ◽  
Computerized Processing ◽  
Fully Automatic ◽  
Diffraction Patterns

Recently, it has become essential to develop a helpful method of the complete crystallographic identification of fine fragmented crystals. This was maainly due to the investigation into structural regularity of large plastic strains. The method should be practicable for determining crystallographic orientation (CO) of elastically stressed micro areas of the order of several micron fractions in size and filled with λ>1010 cm-2 density dislocations or stacking faults. The method must provide the misorientation vectors of the adjacent fragments when the angle ω changes from 0 to 180° with the accuracy of 0,3°. The problem is that the actual electron diffraction patterns obtained from fine fragmented crystals are the superpositions of reflections from various fragments, though more than one or two reflections from a fragment are hardly possible. Finally, the method should afford fully automatic computerized processing of the experimental results.The proposed method meets all the above requirements. It implies the construction for a certain base position of the crystal the orientation matrix (0M) A, which gives a single intercorrelation between the coordinates of the unity vector in the reference coordinate system (RCS) and those of the same vector in the crystal reciprocal lattice base : .

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