Hilbert series of modules of GK-dimension two over elliptic algebras

We characterize the Hilbert functions and minimal resolutions of (critical) Cohen–Macaulay graded right modules of Gelfand–Kirillov dimension two over generic quadratic and cubic three-dimensional Artin–Schelter regular algebras. See also [Y. Berest, G. Wilson, Ideal classes of the Weyl algebra and noncommutative projective geometry (with an appendix by Michel Van den Bergh), Int. Math. Res. Not. 2002 (26) (2002) 1347–1396; L. Le Bruyn, Moduli spaces for right ideals of the Weyl algebra, J. Algebra 172 (1995) 32–48; T.A. Nevins, J.T. Stafford, Sklyanin algebras and Hilbert schemes of points, math.AG/0310045, 2003. [8], [14] and [15]].