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Oka manifolds: From Oka to Stein and back

Franc Forstnerič (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

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 conjecture of Kottwitz and Rapoport

Qëndrim R. Gashi (2010)

Annales scientifiques de l'École Normale Supérieure

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 actions of * on algebraic spaces

Andrzej Bialynicki-Birula (1993)

Annales de l'institut Fourier

The main result of the paper says that all schematic points of the source of an action of C * on an algebraic space X are schematic on X .

On complete intersections

Franc Forstnerič (2001)

Annales de l’institut Fourier

We construct closed complex submanifolds of n which are differential but not holomorphic complete intersections. We also prove a homotopy principle concerning the removal of intersections with certain complex subvarieties of n .

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