Maps from Feigin and Odesskii's elliptic algebras to twisted homogeneous coordinate rings

Abstract The elliptic algebras in the title are connected graded $\mathbb {C}$ -algebras, denoted $Q_{n,k}(E,\tau )$ , depending on a pair of relatively prime integers $n>k\ge 1$ an curve E and point $\tau \in E$ . This paper examines canonical homomorphism from to twisted homogeneous coordinate ring $B(X_{n/k},\sigma ',\mathcal {L}^{\prime }_{n/k})$ characteristic variety $X_{n/k}$ for When is isomorphic $E^g$ or symmetric power $S^gE$ we show that ) \to B(X_{n/k},\sigma surjective, relations generated degrees $\le 3$ noncommutative scheme $\mathrm {Proj}_{nc}(Q_{n,k}(E,\tau ))$ has closed subvariety respectively. $X_{n/k}=E^g$ =0$ results about morphism $\Phi _{|\mathcal {L}_{n/k}|}:E^g \mathbb {P}^{n-1}$ embeds as projectively normal scheme-theoretic intersection quadric cubic hypersurfaces.