4 problems

A klt type variety is a variety that admits a klt pair structure. A polarized endomorphism is an endomorphism $f\colon X\rightarrow X$ for which $f^*A\sim mA$ for some ample diviso…

Minimal-volume conjecture. For every integer $n\geq 2$, $X_n$ has the minimum volume among all klt projective $n$-folds with ample canonical class.

Reflexive differential nonvanishing conjecture. The sheaf $\Omega^{[q]}_X$ is pseudoeffective if and only if there exists a positive integer $m$ such that

Let $X$ be a normal projective klt variety with $H^1(X,\mathcal O_X)=0$ and $K_X\sim_{\mathbb Q}0$, and let $L$ be a nef divisor. Singular abundance conjecture. Then $L$ is semiamp…