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The Hilbert function of curves on certain smooth quartic surfaces. (English) Zbl 0701.14029
Space curves that either lie on a quadratic or cubic surface or on a Mori quartic surface [cf. 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).
Reviewer: J.H.de Boer

MSC:
14H50 Plane and space curves
14C20 Divisors, linear systems, invertible sheaves
14J25 Special surfaces
14C05 Parametrization (Chow and Hilbert schemes)
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References:
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