2 problems

Let $S$ be a minimal compact complex surface of Kodaira class $VII_0$, with first Betti number $b_1(S)=1$, and suppose that $S$ contains more than $0$ rational curves, where…

Let $S$ be a minimal compact complex surface in class $VII_0^+$, meaning $b_1(S)=1$ and $b_2(S)\geq 1$. A GSS conjecture asserts that every such surface contains a global spherical…