On the Rank of Multigraded Differential Modules

Adam Boocher, Justin W. DeVries

A ${\mathbb{Z}}^d$-graded differential $R$-module is a ${\mathbb{Z}}^d$-graded $R$-module $D$ equipped with an endomorphism, $\delta$, that squares to zero. For $R=k[x_1,\dots ,x_d]$, this…