5 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…

Characterization of torus quotient pairs. In the above setting, the following are equivalent: 1. $\mathrm{c}_{1}(K_X+\Delta)=0\in \HH2.X.{\mathbb{R}}.$ and

For a positive integer $n$ and a natural number $d$, let $A(X,D)$ denote the space of admissible sections associated with the divisor $D$. Uniform admissible-section conjecture. If…

KD hypothesis. If $(X,B)\sim_K(Y,C)$, then there is an equivalence

Let $(X,\Delta)$ be a klt pair, meaning that $X$ has Kawamata log terminal singularities and $\Delta$ is the boundary divisor. Abundance conjecture. If … is nef, then $K_X+\Delta$…