∗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.
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.
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-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...
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,...