2 problems

Equivalent formulation. The map $f\cdot:R_w\to M_{w+3m}$ is an isomorphism for every $w\bsin\mathbb{N}$. This is presented as an equivalent linear-algebraic formulation of the weig…

Let $P=\mathbb{C}[x,y,z]$ be a polynomial ring with weights $\operatorname{wt}(x)=1$, $\operatorname{wt}(y)=2$, and $\operatorname{wt}(z)=3$. Let $f\bsin P$ be a general…