Variations of mixed Hodge structure attached to the deformation theory of a complex variation of Hodge structures

Philippe Eyssidieux; Carlos Simpson

Displaying similar documents to “Variations of mixed Hodge structure attached to the deformation theory of a complex variation of Hodge structures”

On the existence of exactly one solution of integral equations in the space $L^{P}$ with a mixed norm

Bogdan Rzepecki (1975)

Annales Polonici Mathematici

Similarity:

Some $R^{N}$ capacities and applications - the lemma on mixed derivatives revisited

J. Korevaar (1986)

Matematički Vesnik

Similarity:

An example of the equation $u_{t} = u_{x x} + f (x, t, u)$ with distinct maximum and minimum solutions of a mixed problem

W. Mlak (1963)

Annales Polonici Mathematici

Similarity:

ℓ¹-Spreading models in subspaces of mixed Tsirelson spaces

Denny H. Leung, Wee-Kee Tang (2006)

Studia Mathematica

Similarity:

We investigate the existence of higher order ℓ¹-spreading models in subspaces of mixed Tsirelson spaces. For instance, we show that the following conditions are equivalent for the mixed Tsirelson space $X = T [{(θ ₙ, ₙ)}_{n = 1}^{\infty}]$ : (1) Every block subspace of X contains an $ℓ ¹ -_{ω}$ -spreading model, (2) The Bourgain ℓ¹-index $I_{b} (Y) = I (Y) > ω^{ω}$ for any block subspace Y of X, (3) $l i m ₘ l i m s u p ₙ θ_{m + n} / θ ₙ > 0$ and every block subspace Y of X contains a block sequence equivalent to a subsequence of the unit vector basis of X. Moreover, if one (and hence all) of these...

Minimality properties of Tsirelson type spaces

Denka Kutzarova, Denny H. Leung, Antonis Manoussakis, Wee-Kee Tang (2008)

Studia Mathematica

Similarity:

We study minimality properties of partly modified mixed Tsirelson spaces. A Banach space with a normalized basis $(e_{k})$ is said to be subsequentially minimal if for every normalized block basis $(x_{k})$ of $(e_{k})$ , there is a further block basis $(y_{k})$ of $(x_{k})$ such that $(y_{k})$ is equivalent to a subsequence of $(e_{k})$ . Sufficient conditions are given for a partly modified mixed Tsirelson space to be subsequentially minimal, and connections with Bourgain’s ℓ¹-index are established. It is also shown that a large class of...

On Clifford-type structures

Wiesław Królikowski

Similarity:

We study several techniques which are well known in the case of Besov and Triebel-Lizorkin spaces and extend them to spaces with dominating mixed smoothness. We use the ideas of Triebel to prove three important decomposition theorems. We deal with so-called atomic, subatomic and wavelet decompositions. All these theorems have much in common. Roughly speaking, they say that a function f belongs to some function space (say $S_{p, q}^{r ̅} A$ ) if, and only if, it can be decomposed as $f (x) = \sum_{ν} \sum_{m} λ_{ν m} a_{ν m} (x)$ , convergence in S’, with...

Hodge type decomposition

Wojciech Kozłowski (2007)

Annales Polonici Mathematici

Similarity:

In the space $Λ^{p}$ of polynomial p-forms in ℝⁿ we introduce some special inner product. Let $H^{p}$ be the space of polynomial p-forms which are both closed and co-closed. We prove in a purely algebraic way that $Λ^{p}$ splits as the direct sum $d * (Λ^{p + 1}) \oplus δ * (Λ^{p - 1}) \oplus H^{p}$ , where d* (resp. δ*) denotes the adjoint operator to d (resp. δ) with respect to that inner product.

Naive boundary strata and nilpotent orbits

Matt Kerr, Gregory Pearlstein (2014)

Annales de l’institut Fourier

Similarity:

We give a Hodge-theoretic parametrization of certain real Lie group orbits in the compact dual of a Mumford-Tate domain, and characterize the orbits which contain a naive limit Hodge filtration. A series of examples are worked out for the groups $S U (2, 1)$ , $S p_{4}$ , and $G_{2}$ .

Function spaces with dominating mixed smoothness

Jan Vybiral

Similarity:

Further new generalized topologies via mixed constructions due to Császár

Erdal Ekici (2015)

Mathematica Bohemica

Similarity:

The theory of generalized topologies was introduced by Á. Császár (2002). In the literature, some authors have introduced and studied generalized topologies and some generalized topologies via generalized topological spaces due to Á. Császár. Also, the notions of mixed constructions based on two generalized topologies were introduced and investigated by Á. Császár (2009). The main aim of this paper is to introduce and study further new generalized topologies called $μ_{12}^{C}$ via mixed constructions...

Subspaces $H_{E}^{p, q, α}$ of mixed-norm spaces $H^{p, q, α}$ of holomorphic functions

M. Jevtić (1985)

Matematički Vesnik

Similarity:

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

Henri Guenancia (2014)

Annales de l’institut Fourier

Similarity:

Let $X$ be a compact Kähler manifold and $Δ$ be a $ℝ$ -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 $(X, Δ)$ .

Mixed $A_{p} - A_{\infty}$ estimates with one supremum

Andrei K. Lerner, Kabe Moen (2013)

Studia Mathematica

Similarity:

We establish several mixed $A_{p} - A_{\infty}$ bounds for Calderón-Zygmund operators that only involve one supremum. We address both cases when the $A_{\infty}$ part of the constant is measured using the exponential-logarithmic definition and using the Fujii-Wilson definition. In particular, we answer a question of the first author and provide an answer, up to a logarithmic factor, to a conjecture of Hytönen and Lacey. Moreover, we give an example to show that our bounds with the logarithmic factors can be arbitrarily...

Distortion and spreading models in modified mixed Tsirelson spaces

S. A. Argyros, I. Deliyanni, A. Manoussakis (2003)

Studia Mathematica

Similarity:

The results of the first part concern the existence of higher order ℓ₁ spreading models in asymptotic ℓ₁ Banach spaces. We sketch the proof of the fact that the mixed Tsirelson space T[(ₙ,θₙ)ₙ], $θ_{n + m} \geq θ ₙ θ ₘ$ and $l i m_{n} θ ₙ^{1 / n} = 1$ , admits an $ℓ ₁^{ω}$ spreading model in every block subspace. We also prove that if X is a Banach space with a basis, with the property that there exists a sequence (θₙ)ₙ ⊂ (0,1) with $l i m_{n} θ ₙ^{1 / n} = 1$ , such that, for every n ∈ ℕ, $| | \sum_{k = 1}^{m} x_{k} | | \geq θ ₙ \sum_{k = 1}^{m} | | x_{k} | |$ for every ₙ-admissible block sequence ${(x_{k})}_{k = 1}^{m}$ of vectors in X, then there exists c...

The generalized Hodge and Bloch conjectures are equivalent for general complete intersections

Claire Voisin (2013)

Annales scientifiques de l'École Normale Supérieure

Similarity:

We prove that Bloch’s conjecture is true for surfaces with $p_{g} = 0$ obtained as $0$ -sets $X_{σ}$ of a section $σ$ of a very ample vector bundle on a variety $X$ with “trivial” Chow groups. We get a similar result in presence of a finite group action, showing that if a projector of the group acts as $0$ on holomorphic $2$ -forms of $X_{σ}$ , then it acts as $0$ on $0$ -cycles of degree $0$ of $X_{σ}$ . In higher dimension, we also prove a similar but conditional result showing that the generalized Hodge conjecture for general $X_{σ}$ ...

On Bressan's conjecture on mixing properties of vector fields

Stefano Bianchini (2006)

Banach Center Publications

Similarity:

In [9], the author considers a sequence of invertible maps $T_{i} : S ¹ \to S ¹$ which exchange the positions of adjacent intervals on the unit circle, and defines as Aₙ the image of the set 0 ≤ x ≤ 1/2 under the action of Tₙ ∘ ... ∘ T₁, (1) Aₙ = (Tₙ ∘ ... ∘ T₁)x₁ ≤ 1/2. Then, if Aₙ is mixed up to scale h, it is proved that (2) $\sum_{i = 1}^{n} (T o t . V a r . (T_{i} - I) + T o t . V a r . (T_{i}^{- 1} - I)) \geq C l o g 1 / h$ . We prove that (1) holds for general quasi incompressible invertible BV maps on ℝ, and that this estimate implies that the map Tₙ ∘ ... ∘ T₁ belongs to the Besov space $B^{0, 1, 1}$ , and its...

Deformations of Kähler manifolds with nonvanishing holomorphic vector fields

Jaume Amorós, Mònica Manjarín, Marcel Nicolau (2012)

Journal of the European Mathematical Society

Similarity:

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...

The diagonal mapping in mixed norm spaces

Guangbin Ren, Jihuai Shi (2004)

Studia Mathematica

Similarity:

For any holomorphic function F in the unit polydisc Uⁿ of ℂⁿ, we consider its restriction to the diagonal, i.e., the function in the unit disc U of ℂ defined by F(z) = F(z,...,z), and prove that the diagonal mapping maps the mixed norm space $H^{p, q, α} (U ⁿ)$ of the polydisc onto the mixed norm space $H^{p, q, | α | + (p / q + 1) (n - 1)} (U)$ of the unit disc for any 0 < p < ∞ and 0 < q ≤ ∞.