O pätnástom Hilbertovom probléme
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 0-dimensional complete intersections.
On a characterization of an abelian variety in the classification theory of algebraic varieties
On a conjecture of Kottwitz and Rapoport
We prove a conjecture of Kottwitz and Rapoport which implies a converse to Mazur’s Inequality for all (connected) split and quasi-split unramified reductive groups. Our results are related to the non-emptiness of certain affine Deligne-Lusztig varieties.
On a geometric property of the normal bundle of surfaces in IP4.
On a theorem of Enriques - Swinnerton-Dyer
On actions of on algebraic spaces
The main result of the paper says that all schematic points of the source of an action of on an algebraic space are schematic on .
On Affine-Ruled Irrational Surfaces.
On Affine-Ruled Rational Surfaces.
On Almost Homogeneous Compact Complex Analytic Surfaces.
On base partitions and cover partitions of skew characters.
On binomial set-theoretic complete intersections in characteristic p.
On chiral differential operators over homogeneous spaces.
On codimension-two subvarieties of hypersurfaces.
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 complete orbit spaces of SL(2) actions
On complete orbit spaces of SL(2) actions, II
The aim of this paper is to extend the results of [BB-Ś2] concerning geometric quotients of actions of SL(2) to the case of good quotients. Thus the results of the present paper can be applied to any action of SL(2) on a complete smooth algebraic variety, while the theorems proved in [BB-Ś2] concerned only special situations.
On congruences of lines in the projective space (Chapter 6 written in collaboration with M. Pedreira)
On covering and quasi-unsplit families of curves
Given a covering family of effective 1-cycles on a complex projective variety , we find conditions allowing one to construct a geometric quotient , with regular on the whole of , such that every fiber of is an equivalence class for the equivalence relation naturally defined by . Among other results, we show that on a normal and -factorial projective variety with canonical singularities and , every covering and quasi-unsplit family of rational curves generates a geometric extremal...