4 problems

Let $X$ be a smooth variety of dimension $n$ and let $L$ be an ample divisor on $X$. For very general points $p_1,\dots,p_r\in X$, write…

Smooth maximal-index conjecture. The largest possible index of any smooth, projective Calabi-Yau $n$-fold is

Non-vanishing conjecture for smooth varieties. The canonical divisor $K_{X}$ has an effective $\mathbb{Q}$-linearly equivalent representative.

Let $X$ be a smooth projective variety. Non-vanishing conjecture. If $K_X$ is pseudo-effective, then there exists an effective $\mathbb{Q}$-divisor $D$ such that … This is the smoo…