A note on ...-constant families of plane curves.
A note on the discriminant of a space curve.
A note on the one-dimensional systems of formal equations
On this paper we compute the numerical function of the approximation theorem of M. Artin for the one-dimensional systems of formal equations.
A Remark on Two-Dimensional Local Rings with the Property of Approximation.
A Rigid Analytic Version of M. Artin's Theorem on Analytic Equations.
Algèbres simples centrales sur les corps de fonctions de deux variables
À toute classe dans le groupe de Brauer d’un corps sont associés deux entiers, l’indice (degré d’un corps gauche représentant la classe) et l’exposant (ordre de la classe dans le groupe de Brauer). L’exposant divise l’indice, mais ne lui est pas nécessairement égal. Lorsque est un corps de nombres, c’est un théorème des années 1930 qu’exposant et indice coïncident. A. J. de Jong (Duke Math. J. 123 (2004) 71-94) a montré récemment qu’ils coïncident aussi lorsque est un corps de fonctions de...
An estimate of approximation constants for p-adic and real varities.
Approximation Properties and Existential Completeness for Ring Morphisms.
Arithmetic on certain quadric bundles of relative dimension 2. I.
Artin Approximation and Formal Fibres of Local Rings.
Binäre Formen und Primideale.
Clôture intégrale des idéaux et équisingularité
This text has two parts. The first one is the essentially unmodified text of our 1973-74 seminar on integral dependence in complex analytic geometry at the Ecole Polytechnique with J-J. Risler’s appendix on the Łojasiewicz exponents in the real-analytic framework. The second part is a short survey of more recent results directly related to the content of the seminar.The first part begins with the definition and elementary properties of the order function associated to an ideal of a reduced analytic...
Concerning the existence of nice components in the Hilbert scheme of curves in ...n for n = 4 and 5.
Darstellbarkeitskriterien für analytische Funktoren
Das formale Prinzip und Modifikationen komplexer Räume.
Deformations of theta divisors and the rank 4 quadrics problem
Deforming syzygies of liftable modules and generalised Knörrer functors
Maps between deformation functors of modules are given which generalise the maps induced by the Knörrer functors. These maps become isomorphisms after introducing certain equations in the target functor restricting the Zariski tangent space. Explicit examples are given on how the isomorphisms extend results about deformation theory and classification of MCM modules to higher dimensions.
Differential equations which come from geometry
Diophantine approximations on projective spaces.
Equisingular deformations of isolated 2-dimensional hyper-surface singularities.