The Main Results

This chapter introduces the objects required for formulating the main results of Lioville-Riemann-Roch type. The results are formulated. In some cases, the Riemann-Roch type equalities cannot be achieved (counterexamples are shown), while inequalities still hold. These inequalities, however, can be applied, the same way the equalities are, for proving the existence of solutions of elliptic equations with prescribed zeros, poles, and growth at infinity.