2 problems

Higher Castelnuovo conjecture. Then $\Gamma$ lies on a curve $D$ of degree at most $n+m-2$. This is related to the Eisenbud–Harris conjecture for curves: the cases $m=1$ and $m=2$…

Let $C$ be a reduced, irreducible, nondegenerate curve of genus $g$ and degree $d$ in ${\bf P}^n$, and let $\pi_\alpha(d,n)$ denote the Eisenbud–Harris bound, with $\alpha$ in the…