We prove that every injective endomorphism of an affine algebraic variety over an algebraically closed field of characteristic zero is an automorphism. We also construct an analytic curve in ℂ⁶ and its holomorphic bijection which is not a biholomorphism.

We show that for a holomorphic foliation with singularities in a projective variety such that every leaf is quasiprojective, the set of rational functions that are constant on the leaves form a field whose transcendence degree equals the codimension of the foliation.

We study an adaptation to the logarithmic case of the Kobayashi-Eisenman pseudo-volume form, or rather an adaptation of its variant defined by Claire Voisin, for which she replaces holomorphic maps by holomorphic $K$-correspondences. We define an intrinsic logarithmic pseudo-volume form ${\Phi }_{X,D}$ for every pair $(X,D)$ consisting of a complex manifold $X$ and a normal crossing Weil divisor $D$ on $X$, the positive part of which is reduced. We then prove that ${\Phi }_{X,D}$ is generically non-degenerate when $X$ is projective and $K_X+D$...

In this paper, we consider an analytic family of holomorphic mappings $f:M\times X\to X$ and the sequence $f^n$ of iterates of $f$. If the sequence is not compactly divergent, there exists an unique retraction $\rho (m,.)$ adherent to the sequence $f{}^n(m,.)$. If $X$ is a strictly convex taut domain in ${\mathbb{C}}^n$ and if the image $\mathrm{\Lambda }\left(\rho \right(m,.\left)\right)$ of $\rho (m,.)$ is of dimension $\ge 1$, we prove that $\mathrm{\Lambda }\left(\rho \right(m,.\left)\right)$ does not depend from $m\in M$. We apply this result to the existence of fixed points of holomorphic mappings on the product of two bounded strictly convex domains.