7 problems

Let $I$ be the ideal of a linear star configuration in a polynomial ring, obtained by choosing arbitrary hyperplanes in projective space. An ideal $I$ is of fiber type if the non-l…

Let ${\mathcal A}=\{H_1,\ldots,H_s\}$ be a generic collection of $s\geq n+1$ hyperplanes in $\mathbb P^n$, with defining linear forms $\ell_1,\ldots,\ell_s$. For $1\leq c\leq n$, l…

Let $d\geq 3$ be an integer, let $F$ be a generic ternary degree $d$ form, and let $\mathbb{X}(d+1)$ denote a star configuration of $d+1$ points in the projective plane. Existence…

Let $cmathbb K$ be a field of characteristic $0$, let $cmathcal C=(cell_1,ldots,cell_n)subset R=cmathbb K[x_1,ldots,x_k]$ be an $[n,k]$-linear code with no zero columns, and let…

Generalized star configuration conjecture. If this equality holds, then $Z$ is either contained in a hyperplane or forms a star configuration of codimension-$c$ subspaces.

Bauer–Szemberg's star configuration conjecture. If this equality holds, then either $\alpha(I)=1$, so that $Z$ is contained in a single hyperplane $H$ in $\mathbb P^n$, or $Z$ cons…

Let $s>n$ and let $\mathcal H=\{H_1,\ldots,H_s\}$ be properly meeting hyperplanes in ${\bf P}^n$, defined by linear forms $L_i$. Let $N+1=s$, let $\mathcal H'$ be the coordinate hy…