4 problems

Let $X$ be a nonsingular projective variety with $\kappa(X)=0$. Ueno's Conjecture K asserts that the Albanese map is birational to an étale fiber bundle over…

Let $X$ satisfy the assumptions that its cotangent bundle contains a nef locally free subsheaf $L^*\subset\Omega_X^1$ proportional to $K_X$. If $\kappa(X)=0$, then the product deco…

Let $S$ be a rank-one log del Pezzo surface, and let $S^0$ denote its smooth locus. A finite étale cover of $S^0$ is affine ruled if it contains an open subset isomorphic to a prod…

Vanishing conjecture for Kollár-hyperbolic varieties. Kollár-hyperbolic varieties satisfy a vanishing theorem: in every nonzero degree, the limit of the normalized dimensions of th…