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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$$X$$.

##### MSC:
 14H50 Plane and space curves 14G15 Finite ground fields in algebraic geometry 14N05 Projective techniques in algebraic geometry
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##### References:
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