Carleman Approximation on Totally Real Subsets of Class Ck.
Characteristic distributions on 4-dimensional almost complex manifolds
In this paper the Nijenhuis tensor characteristic distributions on a non-integrable four-dimensional almost complex manifold is investigated for integrability, singularities and equivalence.
Characteristic divisors on complex manifolds.
Characteristic varieties and vanishing cycles.
Classical Poincaré metric pulled back off singularities using a Chow-type theorem and desingularization
We construct complete Kähler metrics on the nonsingular set of a subvariety of a compact Kähler manifold. To that end, we develop (i) a constructive method for replacing a sequence of blow-ups along smooth centers, with a single blow-up along a product of coherent ideals corresponding to the centers and (ii) an explicit local formula for a Chern form associated to this ‘singular’ blow-up. Our metrics have a particularly simple local formula of a sum of the original metric and of the pull back...
Closed transverse -forms on compact complex manifolds
Codimension one foliations on complex tori
We prove a structure theorem for codimension one singular foliations on complex tori, from which we deduce some dynamical consequences.
Cohomology and splitting of Hermitian-Einstein vector bundles.
Cohomology of the Lie Algebra of Vector Fields on a Complex Manifold.
Compact complex manifolds with numerically effective cotangent bundles.
Compact Kähler manifolds with compactifiable universal cover
In this appendix, we observe that Iitaka’s conjecture fits in the more general context of special manifolds, in which the relevant statements follow from the particular cases of projective and simple manifolds.
Compact Kähler manifolds with nonnegatively curvature operator.
Compact lcK manifolds with parallel vector fields
We show that for n > 2 a compact locally conformally Kähler manifold (M2n , g, J) carrying a nontrivial parallel vector field is either Vaisman, or globally conformally Kähler, determined in an explicit way by a compact Kähler manifold of dimension 2n − 2 and a real function.
Compactness for embedded pseudoholomorphic curves in 3-manifolds
We prove a compactness theorem for holomorphic curves in 4-dimensional symplectizations that have embedded projections to the underlying 3-manifold. It strengthens the cylindrical case of the SFT compactness theorem [BEH+C03] by using intersection theory to show that degenerations of such sequences never give rise to multiple covers or nodes, so transversality is easily achieved. This has application to the theory of stable finite energy foliations introduced in [HWZ03], and also suggests a new...
Complex analytic geometry of complex parallelizable manifolds
Complex Hyperbolic Surfaces of Abelian Type
2000 Mathematics Subject Classification: 11G15, 11G18, 14H52, 14J25, 32L07.We call a complex (quasiprojective) surface of hyperbolic type, iff – after removing finitely many points and/or curves – the universal cover is the complex two-dimensional unit ball. We characterize abelian surfaces which have a birational transform of hyperbolic type by the existence of a reduced divisor with only elliptic curve components and maximal singularity rate (equal to 4). We discover a Picard modular surface of...
Complex structures on product of circle bundles over complex manifolds
Let be a holomorphic line bundle over a compact complex manifold for . Let denote the associated principal circle-bundle with respect to some hermitian inner product on . We construct complex structures on which we refer to as scalar, diagonal, and linear types. While scalar type structures always exist, the more general diagonal but non-scalar type structures are constructed assuming that are equivariant -bundles satisfying some additional conditions. The linear type complex structures...
Complex structures on
Data una varietà Riemanniana orientata , il fibrato principale di basi ortonormali positive su ha una parallelizzazione canonica dipendente dalla connessione di Levi-Civita. Questo fatto suggerisce la definizione di una classe molto naturale di strutture quasi-complesse su . Dopo le necessarie definizioni, discutiamo qui l'integrabilità di queste strutture, esprimendola in termini della struttura Riemanniana .
Complexifications of Transversely Holomorphic.
Concave domains with trivial biholomorphic invariants
It is proved that if F is a convex closed set in ℂⁿ, n ≥2, containing at most one (n-1)-dimensional complex hyperplane, then the Kobayashi metric and the Lempert function of ℂⁿ∖ F identically vanish.