5 problems

Let $E$ be a vector bundle on $\mathbb{P}^1\times\mathbb{P}^1$. It has natural cohomology if, for every pair of integers $(n,m)$, the cohomology of…

Let $X=\mathbb{P}^1\times\mathbb{P}^1$ and let $L=aC_0+bf$. Let $\delta(a,b)$ denote the length of the region of mixed syzygies. Mixed-syzygy length conjecture. The length is … Equ…

Let $Q$ be the quadratic form defining the quadric surface, let $[?]N(B)$ denote the number of rational points of height at most $B$, and let $[?]\Delta_Q$ be its discriminant. Uni…

Effective-divisor spanning conjecture. The method laid out in this paper produces a set of effective divisors spanning the effective cone of $M(\xi)$ for every $\xi$ above Rudakov'…

Uniqueness conjecture. The general ${\mathcal{E}}\in {\mathfrak{M}}(k)$ is uniquely determined by $S({\mathcal{E}})$.