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Holomorphic actions, Kummer examples, and Zimmer program

Serge Cantat, Abdelghani Zeghib (2012)

Annales scientifiques de l'École Normale Supérieure

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

Holomorphic group actions with few compact orbits

Christoph Gellhaus, Tilmann Wurzbacher (2001)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Holomorphic Poisson Cohomology

Zhuo Chen, Daniele Grandini, Yat-Sun Poon (2015)

Complex Manifolds

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...

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

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...

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