5 problems

Let $G$ be a graph, let $\Bbbk$ be a field, and let $R_G$ denote the quotient by the binomial edge ideal associated to $G$. Write $p$ for the characteristic of the base field. Mats…

Let $G$ be a simple graph on $n$ vertices, let $\Bbbk$ be a field, and set $R=\Bbbk[x_{1},\ldots,x_{n},y_{1},\ldots,y_{n}]$. For $\{i,j\}\in E(G)$, write…

5-cycle F-purity conjecture. If $p\geq 3$, then $S/J_{C_5}$ is $F$-pure.

Weak-closedness characterization. The quotient $S/J_G$ is $F$-pure if and only if $G$ is weakly closed.

Log canonicity equals dense $F$-purity conjecture. Log canonicity equals dense $F$-purity for all polynomials.