7 problems

Let $C\subset\mathbb P^3$ be the union of $r$ general lines. The strong Lefschetz property conjecture. Then $M(C)$ has SLP. Here $M(C)$ denotes the Hartshorne–Rao module of $C$, an…

Kleppe–Ellia conjecture. The family $W$ is an irreducible component of $(H(d,g)^{sc})_{\operatorname{red}}$, and $H(d,g)^{sc}$ is generically non-reduced along $W$.

General weighted-homogeneous polynomial ideal conjecture. The ideal $I$ contains no polynomial of standard degree $3m-3$. If true, the construction in the paper would imply the rel…

Let $d \geq 5$ be an integer congruent to $2$ modulo $3$. A primitive $d$-line is a primitive locally Cohen–Macaulay $d$-fold structure supported on a line $L\subset\mathbb{P}^3$;…

For integers $kb5$ and $f\a0\in [k-1,2k-6]$, define … … where $\delta(c)=3$ if $c=1$ or $3$, $\delta(c)=1$ if $c\equiv2\pmod 3$, and $\delta(c)=0$ otherwise. Let $G(d,k)$ be the ma…

Maximal-rank conjecture. There exists a constant $K$ such that, for all natural numbers $d,g$ satisfying

Let $\mathcal{C}_1$ and $\mathcal{C}_2$ be cubic rational helical space curves with proportionality constants $\mu_1$ and $\mu_2$, respectively. The curves have proportionality con…