Displaying similar documents to “Which 3-manifold groups are Kähler 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...

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...

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...

On the volume of a pseudo-effective class and semi-positive properties of the Harder-Narasimhan filtration on a compact Hermitian manifold

Zhiwei Wang (2016)

Annales Polonici Mathematici

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This paper divides into two parts. Let (X,ω) be a compact Hermitian manifold. Firstly, if the Hermitian metric ω satisfies the assumption that ̅ ω k = 0 for all k, we generalize the volume of the cohomology class in the Kähler setting to the Hermitian setting, and prove that the volume is always finite and the Grauert-Riemenschneider type criterion holds true, which is a partial answer to a conjecture posed by Boucksom. Secondly, we observe that if the anticanonical bundle K X - 1 is nef, then for...

Hölder continuous solutions to Monge–Ampère equations

Jean-Pierre Demailly, Sławomir Dinew, Vincent Guedj, Pham Hoang Hiep, Sławomir Kołodziej, Ahmed Zeriahi (2014)

Journal of the European Mathematical Society

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Let ( X , ω ) be a compact Kähler manifold. We obtain uniform Hölder regularity for solutions to the complex Monge-Ampère equation on X with L p right hand side, p > 1 . The same regularity is furthermore proved on the ample locus in any big cohomology class. We also study the range ( X , ω ) of the complex Monge-Ampère operator acting on ω -plurisubharmonic Hölder continuous functions. We show that this set is convex, by sharpening Kołodziej’s result that measures with L p -density belong to ( X , ω ) and proving that...

Towards a Mori theory on compact Kähler threefolds III

Thomas Peternell (2001)

Bulletin de la Société Mathématique de France

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Based on the results of the first two parts to this paper, we prove that the canonical bundle of a minimal Kähler threefold ( K X is nef) is good,its Kodaira dimension equals the numerical Kodaira dimension, (in particular some multiple of K X is generated by global sections); unless X is simple. “Simple“ means that there is no compact subvariety through the very general point of X and X not Kummer. Moreover we show that a compact Kähler threefold with only terminal singularities...

Kähler-Einstein metrics with mixed Poincaré and cone singularities along a normal crossing divisor

Henri Guenancia (2014)

Annales de l’institut Fourier

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Let X be a compact Kähler manifold and Δ be a -divisor with simple normal crossing support and coefficients between 1 / 2 and 1 . Assuming that K X + Δ is ample, we prove the existence and uniqueness of a negatively curved Kahler-Einstein metric on X Supp ( Δ ) having mixed Poincaré and cone singularities according to the coefficients of Δ . As an application we prove a vanishing theorem for certain holomorphic tensor fields attached to the pair ( X , Δ ) .

η -Ricci Solitons on η -Einstein ( L C S ) n -Manifolds

Shyamal Kumar Hui, Debabrata Chakraborty (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The object of the present paper is to study η -Ricci solitons on η -Einstein ( L C S ) n -manifolds. It is shown that if ξ is a recurrent torse forming η -Ricci soliton on an η -Einstein ( L C S ) n -manifold then ξ is (i) concurrent and (ii) Killing vector field.

Lie description of higher obstructions to deforming submanifolds

Marco Manetti (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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To every morphism χ : L M of differential graded Lie algebras we associate a functors of artin rings Def χ whose tangent and obstruction spaces are respectively the first and second cohomology group of the suspension of the mapping cone of χ . Such construction applies to Hilbert and Brill-Noether functors and allow to prove with ease that every higher obstruction to deforming a smooth submanifold of a Kähler manifold is annihilated by the semiregularity map.

Complete Riemannian manifolds admitting a pair of Einstein-Weyl structures

Amalendu Ghosh (2016)

Mathematica Bohemica

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We prove that a connected Riemannian manifold admitting a pair of non-trivial Einstein-Weyl structures ( g , ± ω ) with constant scalar curvature is either Einstein, or the dual field of ω is Killing. Next, let ( M n , g ) be a complete and connected Riemannian manifold of dimension at least 3 admitting a pair of Einstein-Weyl structures ( g , ± ω ) . Then the Einstein-Weyl vector field E (dual to the 1 -form ω ) generates an infinitesimal harmonic transformation if and only if E is Killing.

The Killing Tensors on an n -dimensional Manifold with S L ( n , ) -structure

Sergey E. Stepanov, Irina I. Tsyganok, Marina B. Khripunova (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper we solve the problem of finding integrals of equations determining the Killing tensors on an n -dimensional differentiable manifold M endowed with an equiaffine S L ( n , ) -structure and discuss possible applications of obtained results in Riemannian geometry.

Approximately Einstein ACH metrics, volume renormalization, and an invariant for contact manifolds

Neil Seshadri (2009)

Bulletin de la Société Mathématique de France

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To any smooth compact manifold M endowed with a contact structure H and partially integrable almost CR structure J , we prove the existence and uniqueness, modulo high-order error terms and diffeomorphism action, of an approximately Einstein ACH (asymptotically complex hyperbolic) metric g on M × ( - 1 , 0 ) . We consider the asymptotic expansion, in powers of a special defining function, of the volume of M × ( - 1 , 0 ) with respect to g and prove that the log term coefficient is independent of J (and any choice...

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.

Remarks on the behaviour of higher-order derivations on the gluing of differential spaces

Krzysztof Drachal (2015)

Czechoslovak Mathematical Journal

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This paper is about some geometric properties of the gluing of order k in the category of Sikorski differential spaces, where k is assumed to be an arbitrary natural number. Differential spaces are one of possible generalizations of the concept of an infinitely differentiable manifold. It is known that in many (very important) mathematical models, the manifold structure breaks down. Therefore it is important to introduce a more general concept. In this paper, in particular, the behaviour...

Symplectic critical surfaces in Kähler surfaces

Xiaoli Han, Jiayu Li (2010)

Journal of the European Mathematical Society

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Let M be a Kähler surface and Σ be a closed symplectic surface which is smoothly immersed in M . Let α be the Kähler angle of Σ in M . We first deduce the Euler-Lagrange equation of the functional L = Σ 1 cos α d μ in the class of symplectic surfaces. It is cos 3 α H = ( J ( J cos α ) ) , where H is the mean curvature vector of Σ in M , J is the complex structure compatible with the Kähler form ω in M , which is an elliptic equation. We call such a surface a symplectic critical surface. We show that, if M is a Kähler-Einstein surface...

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.

The gradient flow of Higgs pairs

Jiayu Li, Xi Zhang (2011)

Journal of the European Mathematical Society

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We consider the gradient flow of the Yang–Mills–Higgs functional of Higgs pairs on a Hermitian vector bundle ( E , H 0 ) over a Kähler surface ( M , ω ) , and study the asymptotic behavior of the heat flow for Higgs pairs at infinity. The main result is that the gradient flow with initial condition ( A 0 , φ 0 ) converges, in an appropriate sense which takes into account bubbling phenomena, to a critical point ( A , φ ) of this functional. We also prove that the limiting Higgs pair ( A , φ ) can be extended smoothly to a vector bundle...

Open Subsets of LF-spaces

Kotaro Mine, Katsuro Sakai (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let F = ind lim Fₙ be an infinite-dimensional LF-space with density dens F = τ ( ≥ ℵ ₀) such that some Fₙ is infinite-dimensional and dens Fₙ = τ. It is proved that every open subset of F is homeomorphic to the product of an ℓ₂(τ)-manifold and = i n d l i m (hence the product of an open subset of ℓ₂(τ) and ). As a consequence, any two open sets in F are homeomorphic if they have the same homotopy type.

Spaces of polynomial functions of bounded degrees on an embedded manifold and their duals

Shuzo Izumi (2015)

Annales Polonici Mathematici

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Let (U) denote the algebra of holomorphic functions on an open subset U ⊂ ℂⁿ and Z ⊂ (U) its finite-dimensional vector subspace. By the theory of least spaces of de Boor and Ron, there exists a projection b from the local ring n , b onto the space Z b of germs of elements of Z at b. At a general point b ∈ U its kernel is an ideal and b induces the structure of an Artinian algebra on Z b . In particular, this holds at points where the kth jets of elements of Z form a vector bundle for each k ∈...

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.