Notice
C. Araujo - Foliations and birational geometry (Part 4)
- document 1 document 2 document 3
- niveau 1 niveau 2 niveau 3
Descriptif
In the last few decades, much progress has been made in birational algebraic geometry. The general viewpoint is that complex projective manifolds should be classified according to the behavior of their canonical class. As a result of the minimal model program (MMP), every complex projective manifold can be built up from 3 classes of (possibly singular) projective varieties, namely, varieties $X$ for which $K_X$ satisfies $K_X0$. Projective manifolds $X$ whose anti-canonical class $-K_X$ is ample are called Fano manifolds.
Techniques from the MMP have been successfully applied to the study of global properties of holomorphic foliations. This led, for instance, to Brunella's birational classification of foliations on surfaces, in which the canonical class of the foliation plays a key role. In recent years, much progress has been made in higher dimensions. In particular, there is a well developed theory of Fano foliations, i.e., holomorphic foliations $F$ on complex projective varieties with ample anti-canonical class $-K_F$.
The first half of this mini-course will be devoted to explaining the MMP and reviewing some aspects of the theory of Fano manifolds. In the second half, we will explore the foliated counterpart of this theory, with a special emphasis on Fano foliations.
Intervention
Thème
Documentation
Dans la même collection
-
S. Druel - A decomposition theorem for singular spaces with trivial canonical class (Part 5)
DRUEL Stéphane
The Beauville-Bogomolov decomposition theorem asserts that any compact Kähler manifold with numerically trivial canonical bundle admits an étale cover that decomposes into a product of a torus, an
-
H. Guenancia - A decomposition theorem for singular spaces with trivial canonical class (Part 2)
GUENANCIA Henri
The Beauville-Bogomolov decomposition theorem asserts that any compact Kähler manifold with numerically trivial canonical bundle admits an étale cover that decomposes into a product of a torus, an
-
F. Touzet - About the analytic classification of two dimensional neighborhoods of elliptic curves
TOUZET Frédéric
I will investigate the analytic classification of two dimensional neighborhoods of an elliptic curve C with trivial normal bundle and discuss the existence of foliations having C as a leaf. Joint work
-
A. Höring - A decomposition theorem for singular spaces with trivial canonical class (Part 3)
HöRING Andreas
The Beauville-Bogomolov decomposition theorem asserts that any compact Kähler manifold with numerically trivial canonical bundle admits an étale cover that decomposes into a product of a torus, an
-
C. Spicer - Minimal models of foliations
SPICER Calum
We will discuss some recent work on the minimal model program (MMP) for foliations and explain some applications of the MMP to the study of foliation singularities and to the study of some
-
S. Ghazouani - Isoholonomic foliations of moduli spaces of Riemann surfaces
GHAZOUANI Selim
In this talk, I will introduce families of foliations on the moduli space of Riemann surfaces M_{g,n} which we call Veech foliations. These foliations are defined by identifying M_{g,n} to
-
G. Binyamini - Point counting for foliations over number fields
BINYAMINI Gal
We consider an algebraic $V$ variety and its foliation, both defined over a number field. Given a (compact piece of a) leaf $L$ of the foliation, and a subvariety $W$ of complementary
-
D. Novikov - Wilkie's conjecture for restricted elementary functions
NOVIKOV Dmitriĭ Aleksandrovich
We consider the structure $\mathbb{R}^{RE}$ obtained from $(\mathbb{R},
-
B. Deroin - The Jouanolou foliation
DEROIN Bertrand
I will discuss dynamical properties of the Jouanolou foliation of the complex projective plane in degree two. Joint work with Aurélien Alvarez.
-
A. Belotto da Silva - Singular foliations in sub-Riemannian geometry and the Strong Sard Conjecture
BELOTTO DA SILVA André Ricardo
Given a totally nonholonomic distribution of rank two $\Delta$ on a three-dimensional manifold $M$, it is natural to investigate the size of the set of points $\mathcal{X}^x$ that can be reached
-
L. Meersseman - Kuranishi and Teichmüller
MEERSSEMAN Laurent
Let X be a compact complex manifold. The Kuranishi space of X is an analytic space which encodes every small deformation of X. The Teichmüller space is a topological space formed by the classes
-
J. Demailly - Existence of logarithmic and orbifold jet differentials
DEMAILLY Jean-Pierre
Given a projective algebraic orbifold, one can define associated logarithmic and orbifold jet bundles. These bundles describe the algebraic differential operators that act on germs of curves
Avec les mêmes intervenants et intervenantes
-
C. Araujo - Foliations and birational geometry (Part 3)
ARAUJO Carolina
In the last few decades, much progress has been made in birational algebraic geometry. The general viewpoint is that complex projective manifolds should be classified according to the behavior
-
C. Araujo - Foliations and birational geometry (Part 1)
ARAUJO Carolina
In the last few decades, much progress has been made in birational algebraic geometry. The general viewpoint is that complex projective manifolds should be classified according to the behavior
-
C. Araujo - Foliations and birational geometry (Part 2)
ARAUJO Carolina
In the last few decades, much progress has been made in birational algebraic geometry. The general viewpoint is that complex projective manifolds should be classified according to the behavior
Sur le même thème
-
"Le mathématicien Petre (Pierre) Sergescu, historien des sciences, personnalité du XXe siècle"
HERLéA Alexandre
Alexandre HERLEA est membre de la section « Sciences, histoire des sciences et des techniques et archéologie industrielle » du CTHS. Professeur émérite des universités, membre effectif de l'Académie
-
Webinaire sur la rédaction des PGD
LOUVET Violaine
Rédaction des Plans de Gestion de Données (PGD) sous l’angle des besoins de la communauté mathématique.
-
Alexandre Booms : « Usage de matériel pédagogique adapté en géométrie : une transposition à interro…
« Usage de matériel pédagogique adapté en géométrie : une transposition à interroger ». Alexandre Booms, doctorant (Université de Reims Champagne-Ardenne - Cérep UR 4692)
-
C. Li - Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions
LI Chao
In this talk, I will discuss some recent developments on the topology of closed manifolds admitting Riemannian metrics of positive scalar curvature. In particular, we will prove if a closed PSC
-
Y. Lai - A family of 3d steady gradient Ricci solitons that are flying wings
LAI Yi
We find a family of 3d steady gradient Ricci solitons that are flying wings. This verifies a conjecture by Hamilton. For a 3d flying wing, we show that the scalar curvature does not vanish at
-
T. Ozuch - Noncollapsed degeneration and desingularization of Einstein 4-manifolds
OZUCH Tristan
We study the noncollapsed singularity formation of Einstein 4-manifolds. We prove that any smooth Einstein 4-manifold close to a singular one in a mere Gromov-Hausdorff (GH) sense is the result
-
D. Tewodrose - Limits of Riemannian manifolds satisfying a uniform Kato condition
TEWODROSE David
Presentation of a joint work with G. Carron and I. Mondello where we study Kato limit spaces.
-
A. Mondino - Time-like Ricci curvature bounds via optimal transport
MONDINO Andrea
The goal of the talk is to present a recent work in collaboration with Cavalletti (SISSA) on optimal transport in Lorentzian synthetic spaces. The aim is to set up a “Lorentzian analog” of the
-
M. Lesourd - Positive Scalar Curvature on Noncompact Manifolds and the Positive Mass Theorem
LESOURD Martin
The study of positive scalar curvature on noncompact manifolds has seen significant progress in the last few years. A major role has been played by Gromov's results and conjectures, and in
-
J. Wang - Topological rigidity and positive scalar curvature
WANG Jian
In this talk, we shall describe some topological rigidity and its relationship with positive scalar curvature. Precisely, we will present a proof that a complete contractible 3-manifold with
-
R. Perales - Recent Intrinsic Flat Convergence Theorems
PERALES Raquel
Théorèmes récents de convergence plane intrinsèque
-
J. Fine - Knots, minimal surfaces and J-holomorphic curves
FINE Joël
I will describe work in progress, parts of which are joint with Marcelo Alves. Let L be a knot or link in the 3-sphere. I will explain how one can count minimal surfaces in hyperbolic 4-space