  We define analogues of homogeneous coordinate algebras for noncommutative
two-tori with real multiplication. We prove that the categories of standard
holomorphic vector bundles on such noncommutative tori can be described in
terms of graded modules over appropriate homogeneous coordinate algebras. We
give a criterion for such an algebra to be Koszul and prove that the Koszul
dual algebra also comes from some noncommutative two-torus with real
multiplication. These results are based on the techniques of math.QA/0211262
allowing to interpret all the data in terms of autoequivalences of the derived
categories of coherent sheaves on elliptic curves.
