Classification of singularities at infinity of polynomials of degree 4 in two variables.
On établit la classification topologique des feuilletages holomorphes de codimension 1 singuliers à l’origine de , admettant une intégrale première multiforme du type .
I give a characterization of the pseudoconvex Hartogs domains in that satisfy the equation , where is the second cohomology group of with coefficients in the constant sheaf .
In 1988 it was proved by the first author that the closure of a partially semialgebraic set is partially semialgebraic. The essential tool used in that proof was the regular separation property. Here we give another proof without using this tool, based on the semianalytic L-cone theorem (Theorem 2), a semianalytic analog of the Cartan-Remmert-Stein lemma with parameters.
We prove a structure theorem for codimension one singular foliations on complex tori, from which we deduce some dynamical consequences.