Jörg Winkelmann

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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)
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)
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.
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)