Add to ORKGThis article studies the relation between the geometry of a smooth projective variety and that of its hyperplane sections from the viewpoint of Mori theory. Let X be a smooth projective variety of dimension n≥4 and Y a smooth hyperplane section of X. Thus H2(Y,R)=H2(X,R) by the Lefschetz hyperplane theorem. Let p:Y→Z be a fibration of Y by Fano varieties. The authors prove several results asserting the existence of an extension of p to X under various conditions. In the main case p is the Mori contraction defined by an extremal ray R of the cone of curves NE−−−(Y) of Y in the region KY<0, and p extends iff R is also an extremal ray of NE−−−(X)
In this paper we classify pairs (X; E) with E ample vector bundle of rank r on a smooth variety X o...
We show that being a general fibre of a Mori fibre space (MFS) is a rather restrictive condition for...
Under some positivity assumptions, estension properties of rationally connected fibrations from a su...
Let $X$ be a smooth complex projective variety and let $Z = (s = 0)$ be a smooth submanifold which i...
The philosophy that ``a projective manifold is more special than any of its smooth hyperplane sect...
Let X be a projective variety with Q-factorial terminal singularities and let L be an ample Cartier ...
Let E be an ample vector bundle of rank r on a complex projective manifold X such that there exists ...
This thesis is devoted to the geometry of Fano varieties and projective vector bundles over a smooth...
Cette thèse a pour but de classifier les variétés de Fano X (c'est-à-dire les variétès algébriques d...
Providing an introduction to both classical and modern techniques in projective algebraic geometry, ...
Abstract Lefschetz's theorem on hyperplane sections relates the topology of a complex projectiv...
Let $(\sM,\sL)$ be a smooth $(n+1)$-dimensional variety polarized by an ample and spanned line bundl...
In this thesis, we study the moduli space of morphisms from a smooth, projective and geometrically i...
The celebrated proof of the Hartshorne conjecture by Shigefumi Mori allowed for the study of the geo...
We consider the problem of determining which Fano manifolds can be realised as fibres of a Mori fibr...
In this paper we classify pairs (X; E) with E ample vector bundle of rank r on a smooth variety X o...
We show that being a general fibre of a Mori fibre space (MFS) is a rather restrictive condition for...
Under some positivity assumptions, estension properties of rationally connected fibrations from a su...
Let $X$ be a smooth complex projective variety and let $Z = (s = 0)$ be a smooth submanifold which i...
The philosophy that ``a projective manifold is more special than any of its smooth hyperplane sect...
Let X be a projective variety with Q-factorial terminal singularities and let L be an ample Cartier ...
Let E be an ample vector bundle of rank r on a complex projective manifold X such that there exists ...
This thesis is devoted to the geometry of Fano varieties and projective vector bundles over a smooth...
Cette thèse a pour but de classifier les variétés de Fano X (c'est-à-dire les variétès algébriques d...
Providing an introduction to both classical and modern techniques in projective algebraic geometry, ...
Abstract Lefschetz's theorem on hyperplane sections relates the topology of a complex projectiv...
Let $(\sM,\sL)$ be a smooth $(n+1)$-dimensional variety polarized by an ample and spanned line bundl...
In this thesis, we study the moduli space of morphisms from a smooth, projective and geometrically i...
The celebrated proof of the Hartshorne conjecture by Shigefumi Mori allowed for the study of the geo...
We consider the problem of determining which Fano manifolds can be realised as fibres of a Mori fibr...
In this paper we classify pairs (X; E) with E ample vector bundle of rank r on a smooth variety X o...
We show that being a general fibre of a Mori fibre space (MFS) is a rather restrictive condition for...
Under some positivity assumptions, estension properties of rationally connected fibrations from a su...