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Classification of maximal rank curves in the liaison class \(L_ n\). (English) Zbl 0607.14015
\({\mathbb{L}}_ n\) is the liaison class corresponding to a Hartshorne-Rao module which is n-dimensional in one component and zero elsewhere. A complete list of the possible degrees in each possible shift of the module is given for curves in this class, and also for maximal rank curves. It is shown that for each shift there exists a smooth curve of minimal degree. Smooth maximal rank curves in the class are completely classified in terms of the numerical character of their plane sections, thus generalizing a result of Gruson and Peskine about arithmetically normal curves.

MSC:
14H99 Curves in algebraic geometry
14M99 Special varieties
14N05 Projective techniques in algebraic geometry
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