Multiple fibres of a morphism.
Nadel's Subschemes of Fano Manifolds X with a Picard Group Pic(X) Isomorphic to Z
∗The author supported by Contract NSFR MM 402/1994.In this paper we find a global sufficient condition for suitable subschemes of Fano manifolds to be Nadel’s subschemes. We apply this condition to one-dimensional subschemes of a projective space.
Non-Archimedean analytic curves in Abelian varieties.
Non-deformability of entire curves in projective hypersurfaces of high degree
In this article, we prove that there does not exist a family of maximal rank of entire curves in the universal family of hypersurfaces of degree in the complex projective space . This can be seen as a weak version of the Kobayashi conjecture asserting that a general projective hypersurface of high degree is hyperbolic in the sense of Kobayashi.
Non-embeddable -convex manifolds
We show that every small resolution of a 3-dimensional terminal hypersurface singularity can occur on a non-embeddable -convex manifold.We give an explicit example of a non-embeddable manifold containing an irreducible exceptional rational curve with normal bundle of type . To this end we study small resolutions of -singularities.
Non-existence of proper holomorphic maps between certain complex manifolds.
Non-split almost complex and non-split Riemannian supermanifolds
Non-split almost complex supermanifolds and non-split Riemannian supermanifolds are studied. The first obstacle for a splitting is parametrized by group orbits on an infinite dimensional vector space. For almost complex structures, the existence of a splitting is equivalent to the existence of local coordinates in which the almost complex structure can be represented by a purely numerical matrix, i.e. containing no Grassmann variables. For Riemannian metrics, terms up to degree 2 are allowed in...
Normal pseudoholomorphic curves
First, we give some characterizations of J-hyperbolic points for almost complex manifolds. We apply these characterizations to show that the hyperbolic embeddedness of an almost complex submanifold follows from relative compactness of certain spaces of continuous extensions of pseudoholomorphic curves defined on the punctured unit disc. Next, we define uniformly normal families of pseudoholomorphic curves. We prove extension-convergence theorems for these families similar to those obtained by Kobayashi,...
Notes on the Diederich-Sukhov-Tumanov Normalization for almost complex structures.
Oka manifolds: From Oka to Stein and back
Oka theory has its roots in the classical Oka-Grauert principle whose main result is Grauert’s classification of principal holomorphic fiber bundles over Stein spaces. Modern Oka theory concerns holomorphic maps from Stein manifolds and Stein spaces to Oka manifolds. It has emerged as a subfield of complex geometry in its own right since the appearance of a seminal paper of M. Gromov in 1989.In this expository paper we discuss Oka manifolds and Oka maps. We describe equivalent characterizations...
On a character of the automorphism group of a compact com-plex manifold.
On Brody and entire curves
We discuss an example of an open subset of a torus which admits a dense entire curve, but no dense Brody curve.
On c-actions on compact complex manifolds with many compact orbits.
On complete intersections
We construct closed complex submanifolds of which are differential but not holomorphic complete intersections. We also prove a homotopy principle concerning the removal of intersections with certain complex subvarieties of .
On Complexifications of Differentiable Manifolds.
On D*-extension property of the Hartogs domains.
A complex analytic space is said to have the D*-extension property if and only if any holomorphic map from the punctured disk to the given space extends to a holomorphic map from the whole disk to the same space. A Hartogs domain H over the base X (a complex space) is a subset of X x C where all the fibers over X are disks centered at the origin, possibly of infinite radius. Denote by φ the function giving the logarithm of the reciprocal of the radius of the fibers, so that, when X is pseudoconvex,...
On holomorphically projective mappings from manifolds with equiaffine connection onto Kähler manifolds
In this paper we study fundamental equations of holomorphically projective mappings from manifolds with equiaffine connection onto (pseudo-) Kähler manifolds with respect to the smoothness class of connection and metrics. We show that holomorphically projective mappings preserve the smoothness class of connections and metrics.
On hyper f-structures.
On isometries of the carathéodory and Kobayashi metrics on strongly pseudoconvex domains
Let and be domains in and an isometry for the Kobayashi or Carathéodory metrics. Suppose that extends as a map to . We then prove that is a CR or anti-CR diffeomorphism. It follows that and must be biholomorphic or anti-biholomorphic.
On isometries of the Kobayashi and Carathéodory metrics
This article considers C¹-smooth isometries of the Kobayashi and Carathéodory metrics on domains in ℂⁿ and the extent to which they behave like holomorphic mappings. First we provide an example which suggests that 𝔹ⁿ cannot be mapped isometrically onto a product domain. In addition, we prove several results on continuous extension of C⁰-isometries f : D₁ → D₂ to the closures under purely local assumptions on the boundaries. As an application, we show that there is no C⁰-isometry between a strongly...