3 problems

Let $(X,\Delta)$ be a $d$-dimensional projective log Fano pair over $\mathbb{C}$, and let $\alpha_F((X,\Delta);\Gamma)$ denote the equal-characteristic-zero $F$-alpha invariant. Lo…

Bounded complement approximation conjecture. There is a natural number $N$ depending only on $(X,\Delta)$ and a sequence of prime divisors $\{E_i\}$ over $X$ such that

Fix $n$ and $\rho\geq 2$. Let $(X,D)$ be an $n$-dimensional log Fano manifold, meaning that $X$ is smooth projective, $D$ is a reduced simple normal crossing divisor, and…