Morphisms to noncommutative projective lines

Let $k$ be a field, let ${\sf C}$ $k$-linear abelian category, $\underline{\mathcal{L}}:=\{\mathcal{L}_{i}\}_{i \in \mathbb{Z}}$ sequence of objects in C}$, and $B_{\underline{\mathcal{L}}}$ the associated orbit algebra. We describe sufficient conditions on $\underline{\mathcal{L}}$ such that there is canonical morphism from noncommutative space Proj }B_{\underline{\mathcal{L}}}$ to projective line sense \cite{abstractp1}, generalizing usual construction map scheme $X$ $\mathbb{P}^{1}$ defined by an invertible sheaf $\mathcal{L}$ generated two global sections. then apply our results construct, for every natural number $d>2$, degree cover Piontkovski's $d$th elliptic curve Polishchuk.