5 problems

Let $(X,B)$ be a klt pair. Write $u(KX+B)$ for the numerical dimension and $\kappa{\iota}(KX+B)$ for the invariant Iitaka dimension of $KX+B$. Abundance conjecture. One has … This i…

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…

Rational connectedness conjecture. If $-(K_X+\Delta)$ is strictly nef, then $X$ is rationally connected.

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