7 problems

Log-terminality conjecture. The divisor pair

The $A_n$-base conjecture. If $f\colon (X,C)\to (S,0)$ is a Mori conic bundle, then $(S,0)$ is a Du Val singularity of type $A_n$.

Let $(X,p)$ be a 3-fold terminal singularity with Gorenstein index $m\geq 1$. An exceptional prime divisor $E$ over $X$ has discrepancy $a(E,X)$, and its associated valuation is de…

For each odd integer $n\geq5$, let $s_i$ be the sequence used in the paper, and let $X$ be the $n$-fold in the theorem constructing the Gorenstein terminal weighted projective spac…

For each integer $n\geq 4$, let $s_0=1$ and define the sequence $(s_i)$ as in the paper, and let $X$ be the $n$-fold in the theorem constructing the weighted projective space with…

Terminal extraction conjecture. There exists a prime divisor $E$ over $X\ni x$ and a divisorial contraction $f:Y\to X$ extracting $E$, such that $Y$ is terminal and

Sharp anti-canonical degree conjecture.