8 problems

Let $(E,V)$ be a generated coherent system of type $(n,d,v)$ on a general curve $X$ of genus $g\ge3$, where $n,d,v$ are positive integers and $v>n$. Write $D_{E,V}$ for its dual sp…

Let $G(\alpha;n,d,k)$ denote the moduli space of $\alpha$-stable coherent systems of type $(n,d,k)$ on the projective line. Suppose that $a\ge2$, $1\le t\le n-1$, and $k\ge n$. Mon…

Non-emptiness conjecture. The space $G(\alpha;n,an-t,k)$ is non-empty for some $\alpha>0$ if and only if one of the following holds:

Clifford-type bound conjecture. For every $\mu'$-stable coherent system $(\mathcal{O}_S^{\oplus R}\to F)$ with

Let $C$ be a smooth projective curve of genus $g$, let $r,d,k$ be integers, let $\mathcal{L}$ be a line bundle on $C$ of degree $d$, and let $G(\alpha;r,\mathcal{L},k)$ denote the…

Extended Bertram–Feinberg–Mukai conjecture. One has

$n+1$-section nonemptiness conjecture. If

Strong Butler conjecture. The bundle $D_V(E)$ is stable.