Mardi 2 mai 11:00-12:00 -
Andrei TELEMAN - I2M, Marseille
On the moduli stack of class VII surface
Résumé : Travail en collaboration avec G. Dloussky
The most important gap in the Kodaira-Enriques classification table concerns the Kodaira class VII, e.g. the class of surfaces $X$ having $\mathrmkod(X) =- \infty$, $b_1(X) = 1$.
The main conjecture which (if true) would complete the classification of class VII surfaces, states that any minimal class VII surface with $b_2 > 0$ contains $b_2$ holomorphic curves. A weaker conjecture states that any such surface contains a cycle of curves, and (if true) would complete the classification up to deformation equivalence.
In a series of recent articles I showed that, at least for small $b_2$, the second conjecture can be proved using methods from Donaldson theory. In this talk I will concentrate on minimal class VII surfaces with $b_2\leq 2$, and I will present recent results on the geometry of the corresponding moduli stacks.
Actions de groupes de Schottky sur les variétés homogènes-rationnelles
Résumé : We systematically study Schottky group actions on homogeneous rational manifolds and find two new families besides those given by Nori’s well-known construction. This yields new examples of non-Kähler compact complex manifolds having free fundamental groups. We then investigate their analytic and geometric invariants such as the Kodaira and algebraic dimension, the Picard group and the deformation theory, thus extending results due to Lárusson and to Seade and Verjovsky. As a byproduct, we see that the Schottky construction allows to recover examples of equivariant compactifications of SL(2, C)/Γ for Γ a discrete free loxodromic subgroup of SL(2, C), previously obtained by A. Guillot. (Travail commun avec CHRISTIAN MIEBACH, Calais)