6 problems

Let $I$ be a grade $c$ perfect ideal in a local Noetherian ring $R$. Let $d$ denote the deviation of $I$ and $t$ the minimal number of generators of $\operatorname{Ext}^c(R/I,R)$.…

Let $C$ be a set of two skew lines in $\mathbb{P}^{4}$, spanning a hyperplane $H$, and let $C'$ be another set of two skew lines in $\mathbb{P}^{4}$, spanning a hyperplane $H'$. Tw…

Let $I$ be a homogeneous licci ideal of height $g$ in a polynomial ring $S$ over a field. Let $D$ be the maximal last shift in a minimal homogeneous free resolution of $I$, let…

Let $S={\Bbbk}[x,y,z]$, let $d$ be a positive integer, and let $[S/I]\in\mathrm{Hilb}^d(\mathbb{A}^3)$ be a smoothable point. Broken Gorenstein characterization conjecture. The fol…

Let $\vec{P}=(P_1,\dotsc,P_6)$ be six points in $\mathbb{R}^3$ forming the base, and let $\vec{p}=(p_1,\ldots,p_6)$ be the platform points obtained from the preceding system. After…

Let $\vec{P}=(P_1,\dotsc,P_6)$ be six points in $\mathbb{R}^3$ forming the base, and let $\vec{p}=(p_1,\ldots,p_6)$ be the six platform points. The authors construct a system of eq…