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Let f : C → A be an entire holomorphic curve from the complex plane C into a semiAbelian variety A. It was proved by [No81] that the Zariski closure of f(C) is a translate of a semi-Abelian subvariety of A (logarithmic Bloch-Ochiai’s theorem). Let D be an effective algebraic divisor on A which is compactified to D̄ on a natural compactification Ā of A (see… (More)

- Jörg Winkelmann
- 2000

We study Hilbert’s fourteenth problem from a geometric point of view. Nagata’s celebrated counterexample demonstrates that for an arbitrary group action on a variety the ring of invariant functions need not be isomorphic to the ring of functions of an affine variety. In this paper we will show that nevertheless it is always isomorphic to the ring of… (More)

- Jörg Winkelmann
- 2008

By a classical result of Wang [14] a connected compact complex manifold X has holomorphically trivial tangent bundle if and only if there is a connected complex Lie group G and a discrete subgroup Γ such that X is biholomorphic to the quotient manifold G/Γ. In particular X is homogeneous. If X is Kähler, G must be commutative and the quotient manifold G/Γ… (More)

Applying the Second Main Theorem of [20], we deal with the algebraic degeneracy of entire holomorphic curves f : C → X from the complex plane C into a complex algebraic normal variety X of positive log Kodaira dimension that admits a finite proper morphism to a semi-abelian variety. We will also discuss applications to the Kobayashi hyperbolicity problem.

- Jörg Winkelmann
- 1998

We construct infinite discrete subsets of Stein manifolds with remarkable properties. These generalize results of Rosay and Rudin on discrete subsets of Cn.

We study the Kobayashi pseudodistance for orbifolds, proving an orbifold version of Brody’s theorem and classifying which one-dimensional orbifolds are hyperbolic.

Let ι : C2 ↪→ S be a compactification of the two dimensional complex space C2. By making use of Nevanlinna theoretic methods and the classification of compact complex surfaces K. Kodaira proved in 1971 ([2]) that S is a rational surface. Here we deal with a more general meromorphic map f : Cn → X into a compact complex manifold X of dimension n, whose… (More)

- Jörg Winkelmann
- 2012

— We determine which algebraic surface of logarithmic irregularity 2 admit an algebraically non-degenerate entire curve. Résumé. — Nous déterminons les surfaces algébriques d’irregularité logarithmique 2 qui admettent des courbes entières non-dégénérées.

One of the main objectives of this paper is to address the following question: When is the global CR automorphism group of a CR manifold a Lie group in an appropriate topology? We give here sufficient geometric conditions on a CR manifold M to guarantee that the group of all its smooth (and real-analytic when M is real-analytic) CR automorphisms has the… (More)

We establish the second main theorem with the best truncation level one Tf (r;L(D̄)) N1(r; f∗D) + Tf (r)|| for an entire holomorphic curve f : C → A into a semi-abelian variety A and an arbitrary effective reduced divisor D on A; the low truncation level is important for applications. We will actually prove this for the jet lifts of f . Finally we give some… (More)