Related papers: Symetries birationnelles des surfaces feuilletees
Here we investigate the birational geometry of projective varieties of arbitrary dimension having defective higher secant varieties. We apply the classical tool of tangential projections and we determine natural conditions for uniruledness,…
Let A^2 denote the affine plane over an algebraically closed field of arbitrary characteristic. Besides contributing several new results in the general theory of birational endomorphisms of A^2, this article describes certain classes of…
We define the concept of symplectic foliation on a symplectic manifold and provide a method of constructing many examples, by using asymptotically holomorphic techniques.
We obtain a classification of codimension one holomorphic foliations on $\mathbb P^4$ with degenerate Gauss maps.
We consider a product of three copies of infinite symmetric group and its representations spherical with respect to the diagonal subgroup. We show that such representations generate functors from a certain category of simplicial…
We prove that a finite group acting by birational automorphisms of a non-trivial Severi-Brauer surface over a field of characteristic zero contains a normal abelian subgroup of index at most 3. Also, we find an explicit bound for orders of…
We prove that the foliated Euler caracteristic classifies amenable measured foliations up to those defined by ergodic actions of the euclidian plane.
We study monodromy groups of elliptic fibrations over the projective line.
In this paper we study transversely holomorphic foliations of complex codimension one with some hypothesis on the transverse structure.
We classify nonsingular holomorphic foliations of dimension and codimension one on certain Hopf manifolds. More general, we prove that all nonsingular codimension one distributions on intermediary or generic Hopf manifolds are integrable…
Related to the classification of regular foliations in a complex algebraic surface, we address the problem of classifying the complex surfaces which admit a flat pencil of foliations. On this matter, a classification of flat pencils which…
It is a well-known and elementary fact that a holomorphic function on a compact complex manifold without boundary is necessarily constant. The purpose of the present article is to investigate whether, or to what extent, a similar property…
We study equivariant birationality from the perspective of derived categories. We produce examples of nonlinearizable but stably linearizable actions of finite groups on smooth cubic fourfolds.
We give a classification of absolutely dicritical foliations of cusp type, that is, the germ of singularities of complex foliations in the complex plane topologically equivalent to the singularity given by the level of the meromorphic…
We study non-compact surfaces obtained by gluing strips $\mathbb{R}\times(-1,1)$ with at most countably many boundary intervals along some these intervals. Every such strip possesses a foliation by parallel lines, which gives a foliation on…
We complete the classification, initiated by the second named author, of homogeneous singular Riemannian foliations of spheres that are lifts of foliations produced from Clifford systems.
We find sharp upper bounds on the order of the automorphism group of a hypersurface in complex projective space in every dimension and degree. In each case, we prove that the hypersurface realizing the upper bound is unique up to…
A rational vector field on a complex projective smooth surface $S$ is said to be birationally integrable if it generates, by integration, a one-parameter subgroup of the group $\operatorname{Bir}(S)$ of birational transformations of $S$. We…
We classify holomorphic Cartan geometries on every compact complex curve, and on every compact complex surface which contains a rational curve.
We obtain a local classification of complex homothetic foliations on Kaehler manifolds by complex curves. This is used to construct almost Kaehler, Ricci-flat metrics subject to additional curvature properties.