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Holomorphic 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...

Holomorphic Projective Structures on Compact Complex Surfaces. II.

Takushiro Ochiai, Shoshichi Kobayashi (1981)

Mathematische Annalen

Holomorphic Projective Structures on Compact Complex Surfaces.

Takushiro Ochiai, Shoshichi Kobayashi (1980)

Mathematische Annalen

Holomorphic rank-2 vector bundles on non-Kähler elliptic surfaces

Vasile Brînzănescu, Ruxandra Moraru (2005)

Annales de l’institut Fourier

In this paper, we consider the problem of determining which topological complex rank-2 vector bundles on non-Kähler elliptic surfaces admit holomorphic structures; in particular, we give necessary and sufficient conditions for the existence of holomorphic rank-2 vector bundles on non-{Kä}hler elliptic surfaces.

Holomorphic symmetries

H. Blaine Lawson, Stephen S.-T. Yau (1987)

Annales scientifiques de l'École Normale Supérieure

Holomorphy angles and sectional curvature in Hermitian elliptic planes over fields and tensor products of fields.

Rosenfeld, Boris (2005)

Publications de l'Institut Mathématique. Nouvelle Série

Homology of tropical varieties

Paul Hacking (2008)

Collectanea Mathematica

Homotopieklassifikation einfach zusammenhängender normaler kompakter komplexer Flächen.

Ludger Kaup, Gottfried Barthel (1974)

Mathematische Annalen

Hyperbolicity properties of quotient surfaces by freely operating arithmetic lattices

Eberhard Oeljeklaus, Christina Schmerling (2000)

Annales de l'institut Fourier

Let $D$ be a bounded symmetric domain in $ℂ^{2}$ and $Γ \subset {Aut}^{0} D$ an irreducible arithmetic lattice which operates freely on $D$ . We prove that the cusp–compactification $\overline{X}$ of $X = D / Γ$ is hyperbolic.

Hyperholomorphic connections on coherent sheaves and stability

Misha Verbitsky (2011)

Open Mathematics

Let M be a hyperkähler manifold, and F a reflexive sheaf on M. Assume that F (away from its singularities) admits a connection ▿ with a curvature Θ which is invariant under the standard SU(2)-action on 2-forms. If Θ is square-integrable, such sheaf is called hyperholomorphic. Hyperholomorphic sheaves were studied at great length in [21]. Such sheaves are stable and their singular sets are hyperkähler subvarieties in M. In the present paper, we study sheaves admitting a connection with SU(2)-invariant...

Image of analytic hypersurfaces. II.

Shanyu Ji (1993)

Mathematische Annalen

Infinitesimal variations of hodge structure (I)

James Carlson, Mark Green, Phillip Griffiths, Joe Harris (1983)

Compositio Mathematica

Intersection theory on Deligne-Mumford compactifications

Eduard Looijenga (1992/1993)

Séminaire Bourbaki

Invariance for multiples of the twisted canonical bundle

Benoît Claudon (2007)

Annales de l’institut Fourier

Let $𝒳 \to Δ$ a smooth projective family and $(L, h)$ a pseudo-effective line bundle on $𝒳$ (i.e. with a non-negative curvature current $Θ h L$ ). In its works on invariance of plurigenera, Y.-T. Siu was interested in extending sections of $m K_{𝒳_{0}} + L$ (defined over the central fiber of the family $𝒳_{0}$ ) to sections of $m K_{𝒳} + L$ . In this article we consider the following problem: to extend sections of $m (K_{𝒳} + L)$ . More precisely, we show the following result: assuming the triviality of the multiplier ideal sheaf $ℐ (𝒳_{0}, h_{| 𝒳_{0}})$ , any section of $m (K_{𝒳_{0}} + L)$ extends to $𝒳$ ; in other...

Kähler manifolds with numerically effective Ricci class

Jean-Pierre Demailly, Thomas Peternell, Michael Schneider (1993)

Compositio Mathematica

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

Henri Guenancia (2014)

Annales de l’institut Fourier

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 $(X, Δ)$ .

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