# On the moduli stack of class VII surface

Date(s) : 02/05/2017   iCal
11 h 00 min - 12 h 00 min

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.

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