Géométrie des tissus
Géométrie et suites récurrentes
Géométrie formelle et géométrie algébrique
Géométrie réelle des dessins d’enfant
À tout dessin d’enfant est associé un revêtement ramifié de la droite projective complexe , non ramifié en dehors de 0, 1 et l’infini. Cet article a pour but de décrire la structure algébrique de l’image réciproque de la droite projective réelle par ce revêtement, en termes de la combinatoire du dessin d’enfant. Sont rappelées en annexe les propriétés de la restriction de Weil et des dessins d’enfants utilisées.
Géométrie réelle des dessins d’enfant : une étude des composantes irréductibles
Dans cet article nous nous intéressons aux propriétés des composantes irréductibles associées à la géométrie réelle d’un dessin d’enfant. Plus précisément, nous étudions les composantes irréductibles de la courbe dont l’ensemble des points réels est l’image réciproque de par une fonction de Belyi d’un dessin d’enfant.
Geometrische Deutung der Additionstheoreme der hyperelliptischen Integrale und Functionen 1. Ordnung im System der confocalen Flächen 2. Grades. (Schluss)
Geometrische Deutung der Additionstheoreme der hyperelliptischen Integrale und Functionen 1. Ordnung im System der confocalen Flächen 2. Grades.
Geometry of an étale covering of the -adic upper half plane
We describe the rigid geometry of the first layer in the tower of coverings of the -adic upper half plane constructed by Drinfeld. Using our results, we describe the stable fiber at p of certain Shimura curves.
Geometry of arithmetically Gorenstein curves in P4.
We characterize the postulation character of arithmetically Gorenstein curves in P4. We give conditions under which the curve can be realized in the form mH - K on some ACM surface. Finally, we complement a theorem by Watanabe by showing that any general arithmetically Gorenstein curve in P4 with arbitrary fixed postulation character can be obtained from a line by a series of ascending complete-intersection biliaisons.
Geometry of Puiseux expansions
We consider the space Curv of complex affine lines t ↦ (x,y) = (ϕ(t),ψ(t)) with monic polynomials ϕ, ψ of fixed degrees and a map Expan from Curv to a complex affine space Puis with dim Curv = dim Puis, which is defined by initial Puiseux coefficients of the Puiseux expansion of the curve at infinity. We present some unexpected relations between geometrical properties of the curves (ϕ,ψ) and singularities of the map Expan. For example, the curve (ϕ,ψ) has a cuspidal singularity iff it is a critical...
Geometry of the theta divisor of a compactified jacobian
G-fonctions et théorème d'irreductibilite de Hilbert
Global function fields with many rational places over the quinary field. II
Global units and ideal class groups.
Gonality and Clifford index for real algebraic curves.
Let X be a smooth connected projective curve of genus g defined over R. Here we give bounds for the real gonality of X in terms of the complex gonality of X.
Gonality for stable curves and their maps with a smooth curve as their target
Here we study the deformation theory of some maps f: X → ℙr , r = 1, 2, where X is a nodal curve and f|T is not constant for every irreducible component T of X. For r = 1 we show that the “stratification by gonality” for any subset of [...] with fixed topological type behaves like the stratification by gonality of M g.
Good Embedding Dimensions for Gorenstein Singularities.
Good reduction of elliptic curves in abelian extensions.
Gorenstein liaison of some curves in P4.
Despite the recent advances made in Gorenstein liaison, there are still many open questions for the theory in codimension ≥ 3. In particular we consider the following question: given two curves in Pn with isomorphic deficiency modules (up to shift), can they be evenly Gorenstein linked? The answer for this is yes for curves in P3, due to Rao, but for higher codimension the answer is not known. This paper will look at large classes of curves in P4 with isomorphic deficiency modules and show that...
Graded quaternion symbol equivalence of function fields
We present criteria for a pair of maps to constitute a quaternion-symbol equivalence (or a Hilbert-symbol equivalence if we deal with global function fields) expressed in terms of vanishing of the Clifford invariant. In principle, we prove that a local condition of a quaternion-symbol equivalence can be transcribed from the Brauer group to the Brauer-Wall group.