Related papers: Feuilletages et transformations p\'eriodiques

We establish a general bijective framework for encoding faces of some classical hyperplane arrangements. Precisely, we consider hyperplane arrangements in $\mathbb{R}^n$ whose hyperplanes are all of the form $\{x_i-x_j=s\}$ for some…

We construct a determinantal family of quarto-quartic transformations of a complex projective space of dimension $3$ from trigonal curves of degree $8$ and genus $5$. Moreover we show that the variety of $(4,4)$-birational maps of…

We prove that the higher harmonic signature of an even dimensional oriented Riemannian foliation of a compact Riemannian manifold with coefficients in a leafwise U(p,q)-flat complex bundle is a leafwise homotopy invariant. We also prove the…

We shall show how to decompose, by functorial and canonical fibrations, arbitrary $n$-dimensional complex projective {Although the geometric results apply to compact K\" ahler manifolds without change, we consider here for simplicity this…

In this note, we extend to the singular case some results on the birational geometry of irreducible holomorphic symplectic manifolds.

In this paper, we study holomorphic foliations of degree four on complex projective space $\mathbb{P}^n$, where $n\geq 3$, with a special focus on obtaining a structural theorem for these foliations. Furthermore, for a foliation…

We look at sequences of positive integers that can be realized as degree sequences of iterates of rational dominant maps of smooth projective varieties over arbitrary fields. New constraints on the degree growth of endomorphisms of the…

We give an explicit description of the Godeaux surfaces that admit an involution such that the quotient surface is birational to an Enriques surface; these surfaces give a 6-dimensional unirational irreducible subset of the moduli space of…

The dynamical degree $\lambda(f)$ of a birational transformation $f$ measures the exponential growth rate of the degree of the formulae that define the $n$-th iterate of $f$. We study the set of all dynamical degrees of all birational…

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…

We analyze the weight diagram associated with foliations on the complex projective plane through the Hilbert-Mumford criterion in Geometric Invariant Theory, focusing in particular on invariants such as the algebraic multiplicity and the…

Using Morita type stratifications, we establish a one-to-one correspondence between geometric vector fields on a separated differentiable stack and stratified vector fields on its orbit space. This correspondence enables us to derive a…

In this paper, after explaining some basic aspects of the modern theory of foliations with the aim of describing the celebrated Reeb foliation, we propose the first construction of a comprehensive physical model of it. The construction of…

We study the invariant theory of singular foliations of the projective plane. Our first main result is that a foliation of degree m>1 is not stable only if it has singularities in dimension 1 or contains an isolated singular point with…

We study the topology of the space of smooth codimension one foliations on a closed 3-manifold. We regard this space as the space of integrable plane fields included in the space of all smooth plane fields. It has been known since the late…

An orthogonal involution $\sigma$ on a central simple algebra $A$, after scalar extension to the function field $\mathcal{F}(A)$ of the Severi--Brauer variety of $A$, is adjoint to a quadratic form $q_\sigma$ over $\mathcal{F}(A)$, which is…

We give a lattice-theoretic characterization for a manifold of $\mathrm{OG}10$ type to be birational to some moduli space of (twisted) sheaves on a K3 surface. We apply it to the Li-Pertusi-Zhao variety of $\mathrm{OG}10$ type associated to…

Phylogenetic algebraic geometry is concerned with certain complex projective algebraic varieties derived from finite trees. Real positive points on these varieties represent probabilistic models of evolution. For small trees, we recover…

In this paper we prove strong toroidalization of birational morphisms of 3-folds. Suppose that f:X\to Y is a birational morphism of nonsingular complete 3-folds, and D_Y, D_X are simple normal crossings divisors on Y and X such that…

We present the abelianisation of the birational transformations of the real projective plane.