2 problems

Nonvanishing conjecture. The class $[c_k^\delta]$ is a nonzero multiple of the generator in degree $2k$.

Let $(X,D)$ be a two-dimensional klt pair with $D=\sum_{j=1}^{n}(1-\beta_j)D_j$, and let $g$ be a weak conical Kähler–Einstein metric on $(X,D)$. Let $S=\operatorname{Sing}(X,D)$ b…