Related papers: Uniformisation of foliations by curves

A way to characterize the space of leaves of a foliation in terms of connections is proposed. A particular example of vertex algebra cohomology of codimension one foliations on complex curves is considered.

In order to understand the linearization problem around a leaf of a singular foliation, we extend the familiar holonomy map from the case of regular foliations to the case of singular foliations. To this aim we introduce the notion of…

Stratifications and iterative differential equations are analogues in positive characteristic of complex linear differential equations. There are few explicit examples of stratifications. The main goal of this paper is to construct…

This work provides a curve-based approach to Ulrich bundles on surfaces, establishing a correspondence that characterizes their existence, with a focus on applications to surfaces in $\mathbb{P}^3$.

We study the relationship between singular holomorphic foliations in $(\mathbb{C}^{2},0)$ and their separatrices. Under mild conditions we describe a complete set of analytic invariants characterizing foliations with quasi-homogeneous…

The goal of this paper is to construct universal cohomology classes on the moduli space of stable bundles over a curve when it is not a fine moduli space, i.e. when the rank and degree are not coprime. More precisely, we show that certain…

This paper is devoted, first of all, to give a complete unified proof of the Characterization Theorem for compact generalized $p-$K\"ahler manifolds (Theorem 3.2). The proof is based on the classical duality between "closed" positive forms…

We study the asymptotics of Fubini-Study currents and zeros of random holomorphic sections associated to a sequence of singular Hermitian line bundles on a compact normal Kaehler complex space.

We place the representation variety in the broader context of abelian and nonabelian cohomology. We outline the equivalent constructions of the moduli spaces of flat bundles, of smooth integrable connections, and of holomorphic integrable…

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 relate certain universal curvature identities for Kaehler manifolds to the Euler-Lagrange equations of the scalar invariants which are defined by pairing characteristic forms with powers of the Kaehler form.

We combine classic stability results for foliations with recent results on deformations of Lie groupoids and Lie algebroids to provide a cohomological characterization for rigidity of compact foliations on compact manifolds.

It is well known that positivity properties of the curvature of a vector bundle have implications on the algebro-geometric properties of the bundle, such as numerical positivity, vanishing of higher cohomology leading to existence of global…

This article uses basic homological methods for evaluating examples of compactly supported cohomology groups of line bundles over projective curve.

We give new characterizations of plurisubharmonic functions and Griffiths positivity of holomorphic vector bundles with singular Finsler metrics. As applications, we present a different method to prove plurisubharmonic variation of…

In this paper we study numerical properties of quotients of holomorphic log-tensors.

We study those real $\mathcal{C}^\infty$ foliations in complex surfaces whose leaves are holomorphic curves. The main motivation is to try and understand these foliations in neighborhoods of curves: can we expect the space of foliations in…

We prove a general extension theorem for holomorphic line bundles on reduced complex spaces, equipped with singular hermitian metrics, whose curvature currents can be extended as positive, closed currents. The result has applications to…

Many mathematical models of physical phenomena that have been proposed in recent years require more general spaces than manifolds. When taking into account the symmetry group of the model, we get a reduced model on the (singular) orbit…

Given an holomorphic Higgs bundle on a compact Riemann surface of genus greater than one, we construct a DQ-module supported by the spectral curve associated to this bundle. Then, we relate quantum curves arising in various situations…