Displaying similar documents to “Non-Kähler compact complex manifolds associated to number fields”

An obstruction to homogeneous manifolds being Kähler

Bruce Gilligan (2005)

Annales de l’institut Fourier

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Let G be a connected complex Lie group, H a closed, complex subgroup of G and X : = G / H . Let R be the radical and S a maximal semisimple subgroup of G . Attempts to construct examples of noncompact manifolds X homogeneous under a nontrivial semidirect product G = S R with a not necessarily G -invariant Kähler metric motivated this paper. The S -orbit S / S H in X is Kähler. Thus S H is an algebraic subgroup of S [4]. The Kähler assumption on X ought to imply the S -action on the base Y of any homogeneous fibration...

Partial integrability on Thurston manifolds

Hyeseon Kim (2013)

Annales Polonici Mathematici

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We determine the maximal number of independent holomorphic functions on the Thurston manifolds M 2 r + 2 , r ≥ 1, which are the first discovered compact non-Kähler almost Kähler manifolds. We follow the method which involves analyzing the torsion tensor dθ modθ, where θ = ( θ ¹ , . . . , θ r + 1 ) are independent (1,0)-forms.

Holomorphic actions, Kummer examples, and Zimmer program

Serge Cantat, Abdelghani Zeghib (2012)

Annales scientifiques de l'École Normale Supérieure

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We classify compact Kähler manifolds M of dimension n 3 on which acts a lattice of an almost simple real Lie group of rank n - 1 . This provides a new line in the so-called Zimmer program, and characterizes certain complex tori as compact Kähler manifolds with large automorphisms groups.

Deformations of Kähler manifolds with nonvanishing holomorphic vector fields

Jaume Amorós, Mònica Manjarín, Marcel Nicolau (2012)

Journal of the European Mathematical Society

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We study compact Kähler manifolds X admitting nonvanishing holomorphic vector fields, extending the classical birational classification of projective varieties with tangent vector fields to a classification modulo deformation in the Kähler case, and biholomorphic in the projective case. We introduce and analyze a new class of 𝑡𝑎𝑛𝑔𝑒𝑛𝑡𝑖𝑎𝑙𝑑𝑒𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛𝑠 , and show that they form a smooth subspace in the Kuranishi space of deformations of the complex structure of X . We extend Calabi’s theorem on the structure of...

On the embedding of 1-convex manifolds with 1-dimensional exceptional set

Lucia Alessandrini, Giovanni Bassanelli (2001)

Annales de l’institut Fourier

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In this paper we show that a 1-convex (i.e., strongly pseudoconvex) manifold X , with 1- dimensional exceptional set S and finitely generated second homology group H 2 ( X , ) , is embeddable in m × n if and only if X is Kähler, and this case occurs only when S does not contain any effective curve which is a boundary.

On the Kähler Rank of Compact Complex Surfaces

Matei Toma (2008)

Bulletin de la Société Mathématique de France

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Harvey and Lawson introduced the Kähler rank and computed it in connection to the cone of positive exact currents of bidimension ( 1 , 1 ) for many classes of compact complex surfaces. In this paper we extend these computations to the only further known class of surfaces not considered by them, that of Kato surfaces. Our main tool is the reduction to the dynamics of associated holomorphic contractions ( 2 , 0 ) ( 2 , 0 ) .

Which 3-manifold groups are Kähler groups?

Alexandru Dimca, Alexander Suciu (2009)

Journal of the European Mathematical Society

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The question in the title, first raised by Goldman and Donaldson, was partially answered by Reznikov. We give a complete answer, as follows: if G can be realized as both the fundamental group of a closed 3-manifold and of a compact Kähler manifold, then G must be finite—and thus belongs to the well-known list of finite subgroups of O ( 4 ) , acting freely on S 3 .

Real Monge-Ampère equations and Kähler-Ricci solitons on toric log Fano varieties

Robert J. Berman, Bo Berndtsson (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

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We show, using a direct variational approach, that the second boundary value problem for the Monge-Ampère equation in n with exponential non-linearity and target a convex body P is solvable iff 0 is the barycenter of P . Combined with some toric geometry this confirms, in particular, the (generalized) Yau-Tian-Donaldson conjecture for toric log Fano varieties ( X , Δ ) saying that ( X , Δ ) admits a (singular) Kähler-Einstein metric iff it is K-stable in the algebro-geometric sense. We thus obtain a new...

Convergence in capacity

Pham Hoang Hiep (2008)

Annales Polonici Mathematici

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We prove that if ( Ω ) u j u ( Ω ) in Cₙ-capacity then l i m i n f j ( d d c u j ) n 1 u > - ( d d c u ) n . This result is used to consider the convergence in capacity on bounded hyperconvex domains and compact Kähler manifolds.

About the Calabi problem: a finite-dimensional approach

H.-D. Cao, J. Keller (2013)

Journal of the European Mathematical Society

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Let us consider a projective manifold M n and a smooth volume form Ω on M . We define the gradient flow associated to the problem of Ω -balanced metrics in the quantum formalism, the Ω -balancing flow. At the limit of the quantization, we prove that (see Theorem 1) the Ω -balancing flow converges towards a natural flow in Kähler geometry, the Ω -Kähler flow. We also prove the long time existence of the Ω -Kähler flow and its convergence towards Yau’s solution to the Calabi conjecture of prescribing...

The Kähler Ricci flow on Fano manifolds (I)

Xiuxiong Chen, Bing Wang (2012)

Journal of the European Mathematical Society

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We study the evolution of pluri-anticanonical line bundles K M - ν along the Kähler Ricci flow on a Fano manifold M . Under some special conditions, we show that the convergence of this flow is determined by the properties of the pluri-anticanonical divisors of M . For example, the Kähler Ricci flow on M converges when M is a Fano surface satisfying c 1 2 ( M ) = 1 or c 1 2 ( M ) = 3 . Combined with the works in [CW1] and [CW2], this gives a Ricci flow proof of the Calabi conjecture on Fano surfaces with reductive automorphism...

Holonomy groups of complete flat manifolds

Michał Sadowski (2007)

Banach Center Publications

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We present short direct proofs of two known properties of complete flat manifolds. They say that the diffeomorphism classes of m-dimensional complete flat manifolds form a finite set S C F ( m ) and that each element of S C F ( m ) is represented by a manifold with finite holonomy group.