6 problems

Let $d$ and $c$ be the dimension and absolute coregularity, respectively, and let $(X,D)$ be a klt Calabi–Yau type pair of dimension $d$ and absolute coregularity $c$. Write…

Let $(X,D)$ be a projective klt pair with absolute coregularity $c$. The orbifold fundamental group of the regular locus, denoted by $\pi_1^{\rm reg}(X,D)$, is taken for the orbifo…

Let $X$ be a rationally connected variety of dimension $n$, regularity $r$, and coregularity $c$. Assume that $G:=\pi_1^{\rm reg}(X)$ is finite. Coregularity structure conjecture.…

Let $c$ and $N$ be positive integers. A minimal dlt center of a log Calabi–Yau pair is a minimal log canonical center on a dlt modification of that pair. Boundedness conjecture for…

Let $X$ be an $n$-dimensional Fano type variety of coregularity zero. A $2$-complement $(X,B)$ is a complement with $(X,B)$ log canonical and $2(K_X+B)\sim 0$. Let $(Y,B_Y)$ be the…

Let $c$ be a nonnegative integer, and let $s(c)$ be the $c$-th Sylvester's number. Let $X$ be a Fano type variety of coregularity at most $c$. Bounded-complement conjecture. If…