2 problems

Let $X$ be an $n$-dimensional nonsingular projective algebraic variety over the complex numbers, and let $\Delta=\sum_{i\in I}\Delta_i$ be a reduced simple normal crossing divisor,…

Let $(X,\Delta)$ be a klt pair with nef log-canonical divisor $K_X+\Delta$. The Non-Vanishing conjecture. There exists an integer $m\geq 1$ such that $m(K_X+\Delta)$ is Cartier and…