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Duality of space curves and their tangent surfaces in characteristic \(p>0\). (English) Zbl 0766.14022
Let \(X\) be a nondegenerate curve in projective \(N\)-space over an algebraically closed field. Let \(0=b_ 0<\dots<b_ N\) be the sequence of integers consisting of the possible intersection multiplicities of \(X\) with hyperplanes at a general point of \(X\). In characteristic 0, there is only one possibility for such a sequence, namely \(0,1,\dots,N\). For \(N=3\), in positive characteristic, there are 5 possible types of sequences \(b_ 0,\dots,b_ 3\). The author characterizes these types in terms of the reflexivity (or nonreflexivity) of \(X\) and of its tangent surface Tan\(X\).

14H50 Plane and space curves
14G15 Finite ground fields in algebraic geometry
14N05 Projective techniques in algebraic geometry
Full Text: DOI
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