7 problems

Let $(r,d)$ be integers satisfying … and $(r,d)\notin\{(7,2),(8,2),(9,2),(8,3),(9,3)\}$. Let $l(d,\delta,\mu^r)$ denote the dimension of the space of homogeneous degree-$\delta$ po…

Let $(r,d)$ be integers satisfying … and $(r,d)\notin\{(7,2),(8,2),(9,3)\}$. Let $l(d,\delta,\mu^r)$ denote the dimension of the space of homogeneous degree-$\delta$ polynomials on…

Good postulation conjecture. A finite union of general codimension $2$ linear subspaces in $\mathbb P^N$ has good postulation.

Let $\Gamma$ be any subscheme of a zero-dimensional complete intersection of hypersurfaces of degrees $d_1\leq\dots\leq d_c$ in a projective space $P^c$. Say that $\Gamma$ fails to…

Let $n,d,r\in\mathbb{N}$ with $n\geq r+2\geq 3$. Let $\Pi\cong\mathbb{P}^r\subset\mathbb{P}^n$ and let $X\subset\mathbb{P}^n$ consist of $s\geq 1$ generic lines and one $m$-multipl…

Let $n,d\in\mathbb{N}$ with $n\geq 3$. Let $X\subset \mathbb{P}^n$ be the scheme consisting of $s\geq 1$ generic lines and one generic $m$-multiple line, where $m\geq 2$. A scheme…

Carlini–Catalisano–Geramita conjecture. The exceptional cases in which $X$ does not have maximal rank are exactly those with $2\leq d\leq m$ and $t=m$.