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On compact Kähler surfaces

Nicholas Buchdahl (1999)

Annales de l'institut Fourier

Without relying on the classification of compact complex surfaces, it is proved that every such surface with even first Betti number admits a Kähler metric and that a real form of the classical Nakai-Moishezon criterion holds on the surface.

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 .

On complete orbit spaces of SL(2) actions, II

Andrzej Białynicki-Birula, Joanna Święcicka (1992)

Colloquium Mathematicae

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 component groups of Jacobians of Drinfeld modular curves

Mihran Papikian (2004)

Annales de l'Institut Fourier

Let J 0 ( 𝔫 ) be the Jacobian variety of the Drinfeld modular curve X 0 ( 𝔫 ) over 𝔽 q ( t ) , where 𝔫 is an ideal in 𝔽 q [ t ] . Let 0 B J 0 ( 𝔫 ) A 0 be an exact sequence of abelian varieties. Assume B , as a subvariety of J 0 ( 𝔫 ) , is stable under the action of the Hecke algebra 𝕋 End ( J 0 ( 𝔫 ) ) . We give a criterion which is sufficient for the exactness of the induced sequence of component groups 0 Φ B , Φ J , Φ A , 0 of the Néron models of these abelian varieties over 𝔽 q [ [ 1 t ] ] . This criterion is always satisfied when either A or B is one-dimensional. Moreover, we prove that the sequence...

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