On the moduli stack of class VII surface
Date(s) : 02/05/2017 iCal
11h00 - 12h00
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 $\mathrm{kod}(X) =- \infty$, $b_1(X) = 1$.
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.
Catégories
