Le théorème des zéros en géométries algébrique et analytique réelles
We generalize a theorem of Siciak on the polynomial approximation of the Lelong class to the setting of toric manifolds with an ample line bundle. We also characterize Lelong classes by means of a growth condition on toric manifolds with an ample line bundle and construct an example of a nonample line bundle for which Siciak's theorem does not hold.
Given a positive closed (1,1)-current defined on the regular locus of a projective variety with bounded mass near the singular part of and an irreducible algebraic subset of , we present uniform estimates for the locus inside where the Lelong numbers of are larger than the generic Lelong number of along .
In 1984 L. Lempert showed that the Lempert function and the Carathéodory distance coincide on non-planar bounded strongly linearly convex domains with real-analytic boundaries. Following his paper, we present a slightly modified and more detailed version of the proof. Moreover, the Lempert Theorem is proved for non-planar bounded strongly linearly convex domains.
In this note by using techniques similar to that of [2] and [3], we study the local polynomial convexity of perturbation of union of two totally real planes meeting along a real line.
La condition “ constant” est une condition numérique d’équisingularité introduite par B. Teissier. Celui-ci a démontré dans (Astérisque, 7 & 8 (1973) II. Théorème 3.9) que cette condition implique les conditions de Whitney, nous montrons ici la réciproque.