Duality of space curves and their tangent surfaces in characteristic \(p>0\)
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\(X\).
scientific article; zbMATH DE number 60549
scientific article