3 problems

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…

Eisenbud and Schreyer's conjecture. For any $p(x,y)\in\mathbb{Q}[x,y]$ with $\gamma>0$, there exists a vector bundle $E$ with natural cohomology and Hilbert polynomial

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'…