5 problems

Let $(X,\Delta)$ be a projective log Fano pair over $\mathbb{C}$, and let $(X_p,\Delta_p)$ denote reductions to characteristic $p$ for sufficiently large primes. Let…

Let $\mathcal{G}$ be a log bounded set of couples that is complete under dominant small modifications, and let $\widehat{\mathcal{G}}$ be its K-moduli completion: a couple belongs…

Let $n$ be a positive integer, and let $(X,\Delta)$ be a log canonical Fano pair. Write $\pi_1^{\rm orb}(X,\Delta)$ for its orbifold fundamental group. Jordan conjecture for log ca…

Structure conjecture for sRC quotients. There exists an orbifold morphism

Anticanonical Boundary Conjecture. Suppose $X$ is a klt Fano variety of dimension $n$ with $\delta(X)<1$. Then there is a general $D\in |-K_X|_{\mathbb Q}$ such that…