Höring, Andreas Bastien, Fanny Humphries, Donovan

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 irreducible, simply-connected Calabi-Yau, and holomorphic symplectic manifolds. With the development of the minimal model program, it became clear that s...

Ghazouani, Selim Bastien, Fanny Humphries, Donovan

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 certain moduli spaces of flat structures and were first defined by Bill Veech. I will try to expose their specificities, both of geometric and dynamical nature. ...

Deroin, Bertrand Bastien, Fanny Humphries, Donovan

I will discuss dynamical properties of the Jouanolou foliation of the complex projective plane in degree two. Joint work with Aurélien Alvarez.

Guenancia, Henri Bastien, Fanny Humphries, Donovan

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 irreducible, simply-connected Calabi-Yau, and holomorphic symplectic manifolds. With the development of the minimal model program, it became clear that s...

Araujo, Carolina Bastien, Fanny Humphries, Donovan

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 singu...

Amerik, Ekaterina Bastien, Fanny Humphries, Donovan

Let X be a holomorphic symplectic manifold and D a smooth hypersurface in X. Then the restriction of the symplectic form on D has one-dimensional kernel at each point. This distribution is called the characteristic foliation. I shall survey a few results concerning the possible Zariski closure of a general leaf of this foliation by myself and Campa...

Araujo, Carolina Bastien, Fanny Humphries, Donovan

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 singu...

Meersseman, Laurent Bastien, Fanny Humphries, Donovan

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 of compact complex manifolds diffeomorphic to X up to biholomorphisms smoothly isotopic to the identity. F. Catanese asked when these two spaces are locally...

Demailly, Jean-Pierre Bastien, Fanny Humphries, Donovan

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 satisfying ad hoc ramification conditions. Holomorphic Morse inequalities can be used to derive precise cohomology estimates and, in particular, lower bounds f...

Floris, Enrica Bastien, Fanny Humphries, Donovan

The goal of this minicourse is to introduce MMP for foliations on surfaces and to outline the classification of foliations on projective surfaces up to birational equivalence.