7 problems

Let $f\colon\big(y\in(Y,\Delta_Y)\big)\to\big(x\in(X,\Delta)\big)$ be a finite surjective morphism between klt pairs, and suppose it is crepant, meaning … Let…

Let $f:Y\to X$ be a finite morphism between smooth projective varieties of dimension $n\ge 2$, each having second Betti number $1$. Suppose that $X\not\cong\mathbb{P}^n$. Amerik's…

Let f\colon X\xymatrix@1@=15pt{\ar[r]&} Y be a finite and dominant morphism from a smooth variety $X$ onto a normal variety $Y$. Kollár's conjecture. The variety $Y$ has quotient…

Finite degree formula. The normalized volumes satisfy

Finite-degree multiplication conjecture. The local volumes satisfy

Finite quotient normalized-volume conjecture. The normalized volumes satisfy

Let $X$ be a smooth uniruled projective variety over an algebraically closed field of characteristic $0$, let $L$ be a big and nef $\mathbb Q$-divisor on $X$, and let $f:Y\to X$ be…