Related papers: The logarithmic leaf complex and foliated d-semist…
We study log canonical models of foliated surfaces of general type. In particular, we show that log canonical models of general type and their minimal partial du Val resolutions are bounded. Moreover, we show the valuative criteria of…
We study Lie foliations on compact manifolds whose transverse group is \emph{metabelian} (a natural generalization of the affine group $\GA$ considered in earlier work). We establish a complete classification of $\GA$-Lie foliations in…
We consider slice filtrations in logarithmic motivic homotopy theory. Our main results establish conjectured compatibilities with the Beilinson, BMS, and HKR filtrations on (topological, log) Hochschild homology and related invariants. In…
Deformation theory is treated for locally notherian formal schemes (non necessarily smooth). The cotangent complex is defined in the derived category through the homology localization functor. The basic properties and results of a…
Working in characteristic two, I classify nonsmooth Enriques surfaces with normal crossing singularities. Using Kato's theory of logarithmic structures, I show that such surfaces are smoothable and lift to characteristic zero, provided they…
We first describe the local and global moduli spaces of germs of foliations defined by analytic functions in two variables with p transverse smooth branches, and with integral multiplicities (in the univalued holomorphic case) or complex…
The versal deformation space of a smooth rational curve in a smooth complex threefold is explicitly computed under certain hypotheses. Under an additional hypothesis, the versal deformation space is then shown to be the variety of critical…
This work explores the space of foliations on projective spaces over algebraically closed fields of positive characteristic, with a particular focus on the codimension one case. It describes how the irreducible components of these spaces…
We study primary and secondary invariants of leafwise Dirac operators on foliated bundles. Given such an operator, we begin by considering the associated regular self-adjoint operator $D_m$ on the maximal Connes-Skandalis Hilbert module and…
Given a compact complex manifold $X$, we prove a Baum-Bott type formula for one-dimensional holomorphic foliations on $X$ that are logarithmic along a hypersurface with isolated singularities. We show that the residues of these foliations…
This paper is devoted to the study of codimension two holomorphic foliations and distributions. We prove the stability of complete intersection of codimension two distributions and foliations in the local case. Converserly we show the…
We prove a Baum--Bott type residual formula for one-dimensional holomorphic foliations, and logarithmic along free divisors. More precisely, this provides a Baum--Bott theorem for a foliated triple $(X, \mathcal{F}, D)$, where $\mathcal{F}$…
This work deals with the topological classification of germs of singular foliations on $(\mathbb C^{2},0)$. Working in a suitable class of foliations we fix the topological invariants given by the separatrix set, the Camacho-Sad indices and…
By introducing a new invariant called the set of slidings, we give a complete strict classification of the class of germs of non-dicritical holomorphic foliations in the plan whose Camacho-Sad indices are not rational. Moreover, we will…
We describe the topological types of leaves of generic logarithmic foliations on the complex projective plane. We prove that all leaves, except for a finite many are biholomorphic to $\mathbb{C}$ or homeomorphic to the surface known as Loch…
We will use flat divisors, and canonically associated singular holomorphic foliations, to investigate some of the geometry of compact complex manifolds. The paper is mainly concerned with three distinct problems: the existence of…
We describe the valuations following infinitely near singular points of a (singular) holomorphic foliation in the complex plane. They appear to be those satisfying a generalization of L'Hopital's rule. With them, we characterize dicritical…
The subject is partial resolution of singularities. Given an algebraic variety X (not necessarily equidimensional) in characteristic zero (or, more generally, a pair (X,D), where D is a divisor on X), we construct a functorial…
We use the theory of foliations to study the relative canonical divisor of a normalized inseparable base-change. Our main technical theorem states that it is linearly equivalent to a divisor with positive integer coefficients divisible by…
Let ${\cal L}$ be a local system on the complement $X^{\star}$ of a normal crossing divisor (NCD) $ Y$ in a smooth analytic variety $X$ and let $ j: X^{\star} = X - Y \to X $ denotes the open embedding. The purpose of this paper is to…