4 problems

Let $\mathcal{A}$ be a central arrangement in $\mathbb{K}^{n+1}$. Write $\operatorname{rgin}(J(\mathcal{A}))$ for the generic initial ideal of its Jacobian ideal, and set … A minim…

Let $A$ be a polynomial ring, let $I\subseteq A$ be a $\mathbb{Z}^m$-graded Cartwright–Strumfels ideal, let $\operatorname{gin}(I)$ be its $\mathbb{Z}^m$-graded generic initial ide…

Let $A=\mathbb{K}[x_1,\dots,x_n]$ be a polynomial ring over a field $\mathbb{K}$, let $I\subseteq A$ be a $\mathbb{Z}^m$-graded Cartwright–Sturmfels ideal, and let…

Let $S$ be the polynomial ring with its ${\mathbb Z}^n$-grading, let $I$ be a Cartwright–Sturmfels (CS) ideal, and let $J$ be its ${\mathbb Z}^n$-graded generic initial ideal. The…