5 problems

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…

Let $X$ be an integral separated surface, $C$ an effective Cartier divisor in $X$, and $o$ a closed point in $C$. Assume that $X$ is smooth away from $C$. Write…

Threshold conjecture. One has

Nash's conjecture. Neither $\overline{N}_E$ nor $\overline{N}_F$ is included in the other:

Arc-space component correspondence conjecture. The irreducible components of $\widehat{\operatorname{Arc}}(Z\subset Y)$ are in a natural one-to-one correspondence with the union of…