2 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…