Related papers: Specialness and Isotriviality for Regular Algebrai…

Let $N$ be a compact manifold with a foliation $\mathscr{F}_N$ whose leaves are compact strictly convex projective manifolds. Let $M$ be a compact manifold with a foliation $\mathscr{F}_M$ whose leaves are compact hyperbolic manifolds of…

We characterize property $(N_p)$ on a polarized surface $(X,L)$ with trivial canonical bundle in terms of the (non)existence of certain forbidden subvarieties of $X$.

We describe natural abelian extensions of the Lie algebra $\aut(P)$ of infinitesimal automorphisms of a principal bundle over a compact manifold $M$ and discuss their integrability to corresponding Lie group extensions. Already the case of…

Let $f:M\to M$ be a dynamically coherent partially hyperbolic diffeomorphism whose center foliation has all its leaves compact. We prove that if the unstable bundle of $f$ is one-dimensional, then the volume of center leaves must be bounded…

We study foliations by curves on the three-dimensional projective space with no isolated singularities, which is equivalent to assuming that the conormal sheaf is locally free. We provide a classification of the topological and algebraic…

In this note we study two features of submanifolds (subvarieties) with ample normal bundles in a compact K\"ahler manifold X. First, we study how algebraic X can be, i.e. we investigate the algebraic dimension. Second, we study curves with…

A noncompact (oriented) surface satisfies the condition $(\star)$ if their isolated ends are ''accumulated by genus''. We show that every surface satisfying this condition is homeomorfic to the leaf of a minimal codimension one foliation on…

In this paper, we study affine manifolds endowed with linear foliations. These are foliations defined by vector subspaces invariant by the linear holonomy. We show that an $n$-dimensional compact, complete, and oriented affine manifold…

This article is dedicated to the study of singular codimension $1$ foliations $\mathcal{F}$ on a simplicial complete toric variety $X$ and their pullbacks by dominant rational maps $\varphi:\mathbb{P}^n\dashrightarrow X$. First, we describe…

Let $S$ be a surface with $p_g(S)=q(S)=0$ and endowed with a very ample line bundle $\mathcal O_S(h)$ such that $h^1\big(S,\mathcal O_S(h)\big)=0$. We show that $S$ supports special (often stable) Ulrich bundles of rank $2$, extending a…

Let $X$ be a normal compact K\"ahler space with klt singularities and torsion canonical bundle. We show that $X$ admits arbitrarily small deformations that are projective varieties if its locally trivial deformation space is smooth. We then…

A complex manifold $X$ of dimension $n$ together with an ample vector bundle $E$ on it will be called a {\sf generalized polarized variety}. The adjoint bundle of the pair $(X,E)$ is the line bundle $K_X + det(E)$. We study the positivity…

We prove that, over a smooth quasi-projective curve, the set of non-isotrivial, smooth and projective families of polarized varieties with a fixed Hilbert polynomial and semi-ample canonical bundle is bounded. This extends the boundedness…

Complex supermanifold structures being deformations of the exterior algebra of a holomorphic vector bundle, have been parametrized by orbits of a group on non-abelian cohomology by P. Green. For the case of odd dimension $4$ and $5$ an…

A singular foliation is called a singular Riemannian foliation (SRF) if every geodesic that is perpendicular to one leaf is perpendicular to every leaf it meets. A typical example is the partition of a complete Riemannian manifold into…

We prove that a one-dimensional foliation with generic singularities on a projective space, exhibiting a Lie group transverse structure in the complement of some codimension one algebraic subset is logarithmic, i.e., it is the intersection…

Let M be a (bounded or not) domain of C^n which is complete with respect to a K\"ahler metric, or more generally, a complete K\"ahler manifold with trivial canonical bundle. Let f be a linearly nondegenerate meromorphic map from M to the…

The present work deals with the canonical map of smooth, compact complex surfaces of general type in a polarization of type $(1,2,2)$ on an abelian threefold. A natural and classical question is whether the canonical system of such surfaces…

The main problem addressed in the paper is the Torelli problem for n-dimensional varieties of general type, more specifically for varieties with ample canonical bundle. It asks under which geometrical condition for a variety the period map…

In this article we consider log canonical pairs which are log-smooth. If the corresponding canonical bundle is pseudo-effective, then we show that any quotient of the orbifold cotangent bundle of the pair has a pseudo-effective determinant.…