Related papers: Singular foliations with trivial canonical class

Prescribed rational functions constitute a subset of rational functions satisfying certain symmetry and analyticity conditions. We define and construct explicitly prescribed rational functions-valued bundle $\mathcal{W}_M$ over a smooth…

We prove existence of flips for log canonical foliated pairs of rank one on a Q-factorial projective klt threefold. This, in particular, provides a proof of the existence of a minimal model for a rank one foliation on a threefold for a…

In this paper we prove that the anti-canonical bundle of a holomorphic foliation $\mathcal{F}$ on a complex projective manifold cannot be nef and big if either $\mathcal{F}$ is regular, or $\mathcal{F}$ has a compact leaf. Then we address…

In this note, we study monodromies of algebraic connections on the trivial vector bundle. We prove that on a smooth complex affine curve, any monodromy arises as the underlying local system of an algebraic connection on the trivial bundle.…

We describe an explicit open book decomposition adapted to the canonical contact structure on the unit cotangent bundle of a compact surface.

In his work on birational classification of foliations on projective surfaces, Brunella showed that every regular foliation on a rational surface is algebraically integrable with rational leaves. This led Touzet to conjecture that every…

The number of singularities, counted with multiplicity, of a generic codimension one holomorphic distribution on a compact toric orbifold is determined. As a consequence, we give the classification of regular distributions on rational…

In this paper we prove that a smooth family of canonically polarized manifolds parametrized by a special (in the sense of Campana) quasi-projective variety is isotrivial.

We prove that, under mild restrictions, the space of codimension-one foliations of degree one on a smooth projective complete intersection has two irreducible components of logarithmic type. We also prove that the same conclusion holds for…

We construct a canonical singular hermitian metric with semipositive curvature current on the canonical line bundle of a compact K\"{a}hler manifold with pseudoeffective canonical bundle.

In this note, we introduce the notion of a singular principal G-bundle, associated to a reductive algebraic group G over the complex numbers by means of a faithful representation $\varrho^\p\colon G\lra \SL(V)$. This concept is meant to…

We consider the union of certain irreducible components of cohomological support loci of the canonical bundle, which we call standard. We prove a structure theorem about them and single out some particular cases, recovering and improving…

We compute the Dolbeault and the Bott-Chern cohomology of six dimensional solvmanifolds endowed with a complex structure of splitting type, introduced by Kasuya, and with trivial canonical bundle. We build, following results by Angella and…

We consider singular holomorphic foliations on compact complex surfaces with invariant rational nodal curve of positive self-intersection. Then, under some assumptions, we list all possible foliations.

We study conformal structure and topology of leaves of singular foliations by Riemann surfaces.

Let $\omega$ be a differential $q$-form defining a foliation of codimension $q$ in a projective variety. In this article we study the singular locus of $\omega$ in various settings. We relate a certain type of singularities, which we name…

In this short note we give a complete characterization of a certain class of compact corank one Poisson manifolds, those equipped with a closed one-form defining the symplectic foliation and a closed two-form extending the symplectic form…

We introduce K3 transitions as a geometric approach to studying canonical 3-folds. These transitions link different deformation classes of canonical 3-folds via a combination of birational contractions and smoothings. As applications, we…

We construct a type of transverse deformations of a Vaisman manifold, which preserves the canonical foliation. For this construction we only need a basic 1-form with certain properties. We show that such basic 1-forms exist in abundance.

Given a reflexive sheaf on a mildly singular projective variety, we prove a flatness criterion under certain stability conditions. This implies the algebraicity of leaves for sufficiently stable foliations with numerically trivial canonical…