he fiber at $\bfq=0$ is the $\bbZ$-semigroup scheme $$V_{\mathbf{GL_0},0} := \bfq^{-0}(0)= \operatorname{Sing}_{0\times 0}\times\bbG_m,$$ where $\operatorname{Sing}_{0\times 0}$ represents the singular $0\times 0$-matrices. 