A new example of a compactification of C3.
A note on complex projective threefolds admitting holomorphic contact structures.
Appendix to the article of T. Peternell: the Kodaira dimension of Kummer threefolds
We prove that Kummer threefolds with algebraic dimension have Kodaira dimension 0.
Compact complex threefolds of class L associated to polynomial automorphisms of C3.
We construct new families of non-Kähler compact complex threefolds belonging to Kato's Class L. The construction uses certain polynomial automorphisms of C3. We also study basic properties of our manifolds.
Compact quotients of large domains in complex projective space
We study compact complex manifolds covered by a domain in -dimensional projective space whose complement is non-empty with -dimensional Hausdorff measure zero. Such manifolds only exist for . They do not belong to the class , so they are neither Kähler nor Moishezon, their Kodaira dimension is , their fundamental groups are generalized Kleinian groups, and they are rationally chain connected. We also consider the two main classes of known 3-dimensional examples: Blanchard manifolds, for which...
Compactifications of C3, III.
On holomorphic maps into compact non-Kähler manifolds
We study the extension problem of holomorphic maps of a Hartogs domain with values in a complex manifold . For compact Kähler manifolds as well as various non-Kähler manifolds, the maximal domain of extension for over is contained in a subdomain of . For such manifolds, we define, in this paper, an invariant Hex using the Hausdorff dimensions of the singular sets of ’s and study its properties to deduce informations on the complex structure of .
On the automorphism group of a complex sphere.
On the non-existence of Kähler structures on certain closed and oriented differentiable 6-manifolds.
Structures de Poisson sur les variétés algébriques de dimension trois
The complex structure on a connected sum of S³ x S³ with trivial canonical bundle.
Towards a Mori theory on compact Kähler threefolds III
Based on the results of the first two parts to this paper, we prove that the canonical bundle of a minimal Kähler threefold (i.e. is nef) is good,i.e.its Kodaira dimension equals the numerical Kodaira dimension, (in particular some multiple of is generated by global sections); unless is simple. “Simple“ means that there is no compact subvariety through the very general point of and not Kummer. Moreover we show that a compact Kähler threefold with only terminal singularities whose canonical...
Twistor spaces with a pencil of fundamental divisors.
Vector bundles on non-Kaehler elliptic principal bundles
We study relatively semi-stable vector bundles and their moduli on non-Kähler principal elliptic bundles over compact complex manifolds of arbitrary dimension. The main technical tools used are the twisted Fourier-Mukai transform and a spectral cover construction. For the important example of such principal bundles, the numerical invariants of a 3-dimensional non-Kähler elliptic principal bundle over a primary Kodaira surface are computed.