3 problems

Let $I\subseteq k[x_0,\dots,x_n]$ be a homogeneous radical ideal of big height $h$, and let $\mathcal{M}=(x_0,\dots,x_n)$ be the graded maximal ideal. Stable Harbourne–Huneke conje…

Let $Z a derivesubseteq \mathbb{P}^n$ be a fat point scheme, let $I:=IZ$ be its defining ideal, and let $\mathcal{M}=(x0,\dots,xn)$ be the graded maximal ideal. **Harbourne–Huneke con…

Let $K[\mathbb{P}^{N}]$ be the homogeneous coordinate ring, let $M$ be its homogeneous maximal ideal, and let $I$ be the ideal of a finite set of points $p_i\in\mathbb{P}^{N}$. Evo…