Related papers: Holomorphic foliations with no transversely projec…

We investigate the accumulation to singular points of leaves of codimension one foliations whose normal bundle is ample, with emphasis on the nonexistence of Levi-flat hypersurfaces.

In this paper, we survey recent progress on the Null Penrose Conjecture, including a proof of the conjecture for smooth null cones that are foliated by doubly convex spheres.

We give a "conceptual" approach to Kourganoff's results about foliations with a transverse similarity structure. In particular, we give a proof, understandable by the targeted community, of the very important result classifying the holonomy…

In this paper we study the moduli space of standard holomorphic structures on a noncommutative complex two torus. It will be shown that the moduli space is naturally identified with the moduli space of stable bundles on an elliptic curve.…

We show that various classes of closed manifolds with non-trivial higher homotopy groups do not support (transitive) Anosov diffeomorphisms. In particular we show that a finite product of spheres at least one of which is even-dimensional…

We investigate projective properties of Lorentzian surfaces. In particular, we prove that if T is a non flat torus, then the index of its isometry group in its projective group is at most two. We also prove that any topologically finite…

There is a conjecture, that the torsionfreeness of the module of differentials in a point of an algebraic or algebroid curve should imply that the curve is non singular at that point. A report on the main results is given.

We prove that foliations on the projective plane admitting a Liouvillian first integral but not admitting a rational first integral always have invariant algebraic curves of degree bounded by a function of the degree of the foliation. We…

We construct families of non-trivial universal rigid secondary classes for foliations, and then discuss their application to prove that foliations are not homotopic. An observation of Lawson about the non-triviality of the normal Pontrjagin…

We show that a non-wandering endomorphism of the torus with invertible linear part without invariant directions and for which the critical points are in some sense generic is transitive. This improves a result of Andersson by allowing…

For every $n$, we construct two curves in the plane that intersect at least $n$ times and do not form spirals. The construction is in three stages: we first exhibit closed curves on the torus that do not form double spirals, then arcs on…

We study surjective endomorphisms of projective bundles over toric varieties, achieving three main results. First, we provide a structural theorem describing endomorphisms of projectivized split bundles over arbitrary base varieties, which…

We construct projective moduli spaces for torsion-free sheaves on noncommutative projective planes. These moduli spaces vary smoothly in the parameters describing the noncommutative plane and have good properties analogous to those of…

We give a new construction of noncommutative surfaces via elliptic difference operators, attaching a 1-parameter noncommutative deformation to any projective rational surface with smooth anticanonical curve. The construction agrees with one…

We prove that, if $f$ is a homeomorphism of the two torus isotopic to the identity whose rotation set is a non-degenerate segment and $f$ has a periodic point, then it has uniformly bounded deviations in the direction perpendicular to the…

We give a geometric obstruction to the non-negativity of the sectional curvature in the total spaces of certain Riemannian submersions with totally geodesic fibers; applications of this obstruction to several examples are given.

The purpose of this note is to present a construction of an infinite family of symplectic tori T_{p} representing an arbitrary multiple of the homology class of the fiber of an elliptic surface E(n), for n > 2, such that, for i \neq j,…

We show that any noncompact oriented surface is homeomorphic to the leaf of a minimal foliation of a closed $3$-manifold. These foliations are (or are covered by) suspensions of continuous minimal actions of surface groups on the circle.…

We classify projective manifolds with flat holomorphic conformal structures.

We prove two theorems on the removal of singularities on the boundary of a pseudo-holomorphic curve. In one theorem, we need no apriori assumption on the area of the curve. The proof uses a doubling argument with the goal of converting…