6 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…

Let $\mathcal{C}\subset\operatorname{\mathbb{P}}^r$, let $\mathbb{L}$ be its unique trisecant line, and set … Assume these objects are as in the paper's second main theorem. The ra…

Let $\widetilde{\mathcal{C}}$ be the rational normal curve and let $p\in\operatorname{\mathbb{P}}^{r+1}\setminus\widetilde{\mathcal{C}}^3$ be a projection center, with…

Oka's conjecture. The Milnor fiber $F$ is simply connected. Equivalently,

Let $q$ and $r$ be nonnegative integers, let $f\in\mathcal M(q+2r,q;2)$, and let … Write $\alpha=\sharp V$ for the number of points of $V$. The possible-zero-count claim. The possi…