Holomorphic Automorphisms of Compact Kähler Surfaces and Their Induced Actions in Cohomology.
Holomorphic Conformal Structures and Uniformization of Complex Surfaces.
Holomorphic equivariant cohomology.
Holomorphic group actions with few compact orbits
Holomorphic Poisson Cohomology
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.
Holomorphic Projective Structures on Compact Complex Surfaces.
Holomorphic rank-2 vector bundles on non-Kähler elliptic surfaces
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
Holomorphy angles and sectional curvature in Hermitian elliptic planes over fields and tensor products of fields.
Homology of tropical varieties
Homotopieklassifikation einfach zusammenhängender normaler kompakter komplexer Flächen.
Hyperbolicity properties of quotient surfaces by freely operating arithmetic lattices
Let be a bounded symmetric domain in and an irreducible arithmetic lattice which operates freely on . We prove that the cusp–compactification of is hyperbolic.
Hyperholomorphic connections on coherent sheaves and stability
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.
Infinitesimal variations of hodge structure (I)
Intersection theory on Deligne-Mumford compactifications
Invariance for multiples of the twisted canonical bundle
Let a smooth projective family and a pseudo-effective line bundle on (i.e. with a non-negative curvature current ). In its works on invariance of plurigenera, Y.-T. Siu was interested in extending sections of (defined over the central fiber of the family ) to sections of . In this article we consider the following problem: to extend sections of . More precisely, we show the following result: assuming the triviality of the multiplier ideal sheaf , any section of extends to ; in other...
Kähler manifolds with numerically effective Ricci class
Kähler-Einstein metrics with mixed Poincaré and cone singularities along a normal crossing divisor
Let be a compact Kähler manifold and be a -divisor with simple normal crossing support and coefficients between and . Assuming that is ample, we prove the existence and uniqueness of a negatively curved Kahler-Einstein metric on having mixed Poincaré and cone singularities according to the coefficients of . As an application we prove a vanishing theorem for certain holomorphic tensor fields attached to the pair .