5 problems

A compact complex surface in class VII$_0^+$ is a surface with first Betti number one and positive second Betti number. A Kato surface is a compact complex surface obtained by Kato…

Let $S$ be a compact complex surface in class $VII_0$, and let $\mathcal T(S)=]a,b[$, with $-\infty\leq a$ and $b<0$, be the moduli space of locally conformally symplectic structur…

Global spherical shell conjecture. Every class $\mathrm{VII}_0$ surface $X$ with

Let $(M^4,J)$ be a compact Class $\mathrm{VII}_+$ surface, let $\omega_0$ be a pluriclosed metric on $M$, and let $p\in M$ be a generic point as described in the surrounding discus…

Kato-surface characterization conjecture. Any minimal class VII surface with $b_2>0$ containing a cycle of rational curves is a Kato surface.