4 problems

Let $X$ be a projective contact manifold with nef canonical divisor $K_X$. Since projective contact manifolds have $\kappa(X)=-\infty$, the abundance conjecture predicts that this…

Let $X$ be an $n$-dimensional projective variety with only terminal singularities. A $\mathbb{Q}$-Cartier divisor $D$ is almost numerically positive if there is a union $F$ of at m…

Let $X$ be a normal projective variety with mild singularities, for example canonical singularities, such that $K_X$ is $\mathbb{Q}$-Cartier and nef. The Kodaira dimension is denot…

Let $d$ be a natural number and let $\mathfrak{R}\subset [0,1]$ be a finite set of rational numbers. For a finite set $\mathfrak{R}$, write … A pair $(X,B)$ is semi-log canonical i…