7 problems

Let $V$ be a Fano variety with log terminal singularities. A variety is rationally connected when any two general points are connected by an irreducible rational curve. Zhang's con…

Let $V$ be a Fano variety with at worst log terminal singularities, and let $V^0$ denote its smooth locus. Zhang's conjecture. The topological fundamental group $\pi_1(V^0)$ is fin…

Let $Y$ be a relatively minimal log terminal variety, and let $Y^0$ denote its smooth locus. The logarithmic Kodaira dimension $4\kappa(Y^0)4$ is considered together with the canon…

The log-terminal anticanonical divisor conjecture. For every $n\in\mathbb{N}$, there exists a divisor $D\in |-nK_X|$ such that

Let $Y$ be an irreducible $\mathbb{Q}$-Gorenstein variety, and let … be a crepant resolution such that $\mathcal{X}$ has affine diagonal. Optimality conjecture for crepant resoluti…

Finiteness conjecture. The local fundamental group of a log terminal singularity is finite.

Density conjecture. The intersection $I_l\cap J$ is dense for every $l$.