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The equations of space curves on a quadric. (English) Zbl 1122.14023

Here the authors give explicit equations for any curve (i.e. pure one-dimensional locally Cohen-Macaulay subscheme) on any quadric surface \(Q\). When \(Q\) is a double plane, this was done by N. Chiarli, S. Greco and U. Nagel [J. Pure Appl. Algebra 190, No. 1–3, 45–57 (2004; Zbl 1064.14029)], which generalizes [R. Harshorne and E. Schlesinger, Commun. Algebra 28, No. 12, 5655–5676 (2000; Zbl 0994.14003)].
This is a very natural problem, because such curves arise quite often (e.g. as the ones with extremal properties) and giving “equations” means also giving “parameter spaces”. As an application they give all Hartshorne-Rao modules of space curves lying on a quadric surface.

MSC:

14H50 Plane and space curves
13D45 Local cohomology and commutative rings
14M06 Linkage
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