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Stéphane Druel

Publications and source records attributed to Stéphane Druel.

34 records · Page 2Linked to original sources
arXiv2015

Locally unsplit families of rational curves of large anticanonical degree on Fano manifolds

In this paper we address Fano manifolds X with a locally unsplit dominating family of rational curves of anticanonical degree equal to the dimension of X. We first observe that their Picard number is at most 3, and then we provide a classification of all cases with maximal Picard number. We also give examples of locally unsplit dominating families of rational curves whose varieties of minimal tangents at a general point is singular.

math.AG↗
arXiv2014

On Fano foliations 2

In this paper we study mildly singular del Pezzo foliations on complex projective manifolds with Picard number one

math.AG↗
arXiv2014

On codimension 1 del Pezzo foliations on varieties with mild singularities

In this paper we extend to the singular setting the theory of Fano foliations developed in our previous paper. A Q-Fano foliation on a complex projective variety X is a foliation F whose anti-canonical class is an ample Q-Cartier divisor. In the spirit of Kobayashi-Ochiai Theorem, we prove that under some conditions the index i of a Q-Fano foliation is bounded by the rank r of F, and classify the cases in which i=r. Next we consider Q-Fano foliations F for which i=r-1. These are called del Pezzo foliations. We classify codimension 1 del Pezzo foliations on mildly singular varieties.

math.AG↗
arXiv2012

On Fano foliations

In this paper we address Fano foliations on complex projective varieties. These are foliations whose anti-canonical class is ample. We focus our attention on a special class of Fano foliations, namely del Pezzo foliations on complex projective manifolds. We show that these foliations are algebraically integrable, with one exceptional case when the ambient space is a projective space. We also provide a classification of del Pezzo foliations with mild singularities.

math.AG↗
arXiv2003

Caractérisation de l'espace projectif

The purpose of this paper is to prove the following theorem. Let $X$ be a projective normal variety defined over an algebraically closed field of characteristic zero and let $Ω_{X}^{1}\to L$ be a one-dimensional foliation on $X$. If $L\cdot C<0$ for all curves $C\subset X$ then either the foliation is regular or else $X$ is a cone over a normal projective variety. This strengthens Wahl's well-known cohomological characterization of the projective space and gives a geometric proof of his results.

math.AG↗
arXiv2000

Espace des modules des faisceaux semi-stables de rang 2 et de classes de Chern $c_{1}=0$, $c_{2}=2$ et $c_{3}=0$ sur une hypersurface cubique lisse de $\mathbb{P}^{4}$

In this note we study the moduli space of rank two semistable sheaves on a smooth cubic hypersurface $X\subset\mathbb{P}^{4}$ with $c_{1}=0$, $c_{2}=2$ and $c_{3}=0$. We show that it is isomorphic to the blow-up of the intermediate jacobian $J(X)$ of $X$ along the Fano surface of $X$. We complete previous results of Iliev-Markushevich AG/9910058 and Markushevich-Tikhomirov AG/9910063.

math.AG↗
arXiv1999

Variétés algébriques dont le fibré tangent est totalement décomposé

Nous montrons que le revêtement universel des variétés algébriques projectives dont le fibré tangent est totalement décomposé et vérifie certaines conditions d'intégrabilité est produit de surfaces de Riemann et que la décomposition de $T_{X}$ est induite par la décomposition du tangent au revêtement universel; lorsque la variété est minimale les conditions d'intégrabilité ne sont pas nécéssaires.

math.AG↗