Galois groups of fields of definition of solvable branched coverings
Galois structure of de Rham cohomology
Gaussian maps for double coverings.
Generalized Mukai conjecture for special Fano varieties
Let X be a Fano variety of dimension n, pseudoindex i X and Picard number ρX. A generalization of a conjecture of Mukai says that ρX(i X−1)≤n. We prove that the conjecture holds for a variety X of pseudoindex i X≥n+3/3 if X admits an unsplit covering family of rational curves; we also prove that this condition is satisfied if ρX> and either X has a fiber type extremal contraction or has not small extremal contractions. Finally we prove that the conjecture holds if X has dimension five.
Generic Curves of Small Genus in IP3 are of Maximal Rank.
Generic simple coverings of the affine plane
Generic Zariski surfaces
Genre et genre residuel des corps de fonctions values.
Geography of log models: theory and applications
This is an introduction to geography of log models with applications to positive cones of Fano type (FT) varieties and to geometry of minimal models and Mori fibrations.
Geometric and arithmetic properties of the Hénon map.
Geometric stability of the cotangent bundle and the universal cover of a projective manifold
We first prove a strengthening of Miyaoka’s generic semi-positivity theorem: the quotients of the tensor powers of the cotangent bundle of a non-uniruled complex projective manifold have a pseudo-effective (instead of generically nef) determinant. A first consequence is that is of general type if its cotangent bundle contains a subsheaf with ‘big’ determinant. Among other applications, we deduce that if the universal cover of is not covered by compact positive-dimensional analytic subsets,...
Geometry and deformation of special Schubert varieties
Global minimal models for endomorphisms of projective space
We prove the existence of global minimal models for endomorphisms of projective space defined over the field of fractions of a principal ideal domain.
Graded Betti numbers of some embedded rational n-folds.
Groupes de Cremona, connexité et simplicité
Le groupe de Cremona est connexe en toute dimension et, muni de sa topologie, il est simple en dimension .
Groupes de Galois de corps de type fini
Il y a quelques années, Florian Pop a démontré que tout corps de type fini sur le corps premier est déterminé à isomorphisme près par son groupe de Galois absolu (quitte à passer à une extension purement inséparable en caractéristique positive). Ce théorème, dont la généalogie remonte à des travaux de Neukirch sur les groupes de Galois de corps de nombres au début des années 1970, répond positivement à la “conjecture anabélienne birationnelle”de A. Grothendieck formulée en 1983. Dans un travail...
Groups of components of Néron models of jacobians