Ivan Pan

Les transformations de Cremona stellaires

We construct the Cremona transformations of Pn satisfying the following property: there exist P1, P2 ∈ Pn such that the image of all straight lines through P1 are straight lines through P2. We characterise these transformations, and for all non-negative integer d we give a formula for the dimension of the set of those whose degree is d.

On the Monomial Birational Maps of the Projective Space

We describe the group structure of monomial Cremona transformations. It follows that every element of this group is a product of quadratic monomial transformations, and geometric descriptions in terms of fans.

On birational transformations of pairs in the complex plane

This article deals with the study of the birational transformations of the projective complex plane which leave invariant an irreducible algebraic curve. We try to describe the state of the art and provide some new results on this subject.

Sur le multidegré des transformations de Cremona

We define a notion of multidegree for Cremona transformations. We show Diophantine inequalities for the multidegree and we construct, in dimension three, the Cremona transformations with all possible multidegrees.© 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS

Foliations with radial Kupka set and pencils of Calabi–Yau hypersurfaces

We show that holomorphic singular codimension one foliations of the complex projective space with a Kupka singular set of radial type and verifying some global hypotheses have rational rst integral. The generic elements of such pencils of hypersurfaces are Calabi-Yau.

Some typical classes of t-norms and the 1-Lipschitz Condition

This paper studies the relation between the satisfaction of the Lipschitz condition by t-norms for constant 1 (1- Lipschitz condition) and some other properties of t-norms. In this sense, we will consider some well know classes of continuous t-norms, such as Archimedean and non Archimedean, and the nilpotent and strict subclasses of Archimedean t-norms. Also will be proved that the unique automorphism which preserves the 1- Lipschitz condition of any t-norm is the identity.