The Hilbert function of curves on certain smooth quartic surfaces (Q913877)

Space curves that either lie on a quadratic or cubic surface or on a Mori quartic surface [cf. \textit{S. Mori}, Nagoya Math. J. 96, 127-132 (1984; Zbl 0576.14032)] give all possible combinations (d,g) of degree and genus that can occur for a space curve. For smooth quartic surfaces that contain only finitely many integral isolated curves - which, as is shown, is the case for Mori surfaces - an algorithm is given to determine the dimension of any complete linear system of divisors on the surface. Hence the Hilbert function of any integral curve on a Mori quartic can be determined (as is the case for curves on a quadric or cubic surface).