Jörg Winkelmann

Nevanlinna theory in several complex variables and Diophantine approximation

Nevanlinna Theory of Meromorphic Functions.- First Main Theorem.- Differentiably Non-Degenerate Meromorphic Maps.- Entire Curves into Algebraic Varieties.- Semi-Abelian Varieties.- Entire Curves into Semi-Abelian Varieties.- Kobayashi Hyperbolicity.- Nevanlinna Theory over Function Fields.- Diophantine Approximation.- Bibliography.- Index.- Symbols

The second main theorem for holomorphic curves into semiabelian varieties II

Abstract We establish the second main theorem with the best truncation level one for the k-jet lift Jk (ƒ) : → Jk (A) of an algebraically non-degenerate entire holomorphic curve ƒ : → A into a semi-abelian variety A and an arbitrary algebraic reduced subvariety Z of Jk (A); the low truncation level is important for applications. Finally we give some applications, including the solution of a problem posed by Mark Green (1974). 2000 Mathematics Subject Classification: 32H30.

Generic subgroups of Lie groups

Abstract We investigate properties of generically choosen finitely generated subgroups of real Lie groups. In particular we ask whether discreteness is generic.

The value distribution of holomorphic curves into semi-Abelian varieties

Abstract Let f: C →A be an entire holomorphic curve into a semi-Abelian variety A . Then the Zariski closure of f( C ) is a translate of a semi-Abelian subvariety of A (logarithmic Bloch–Ochiais theorem). We establish a quantitative version of the above result for such f , i.e., the second main theorem and the defect relation.

Quasiprojective varieties admitting Zariski dense entire holomorphic curves

Abstract. Let X

Holomorphic self-maps of parallelizable manifolds

X

Nevanlinna Theory over Function Fields

be a complex quasiprojective variety. A result of Noguchi–Winkelmann–Yamanoi shows that if X

The First Main Theorem

X

Nevanlinna Theory of Meromorphic Functions

admits a Zariski dense entire curve, then its quasi-Albanese map is a fiber space. We show that the orbifold structure induced by a proper birationally equivalent map on the base is special in this case. As a consequence, if X

Entire Curves in Semi-abelian Varieties

X