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On the inseparable degree of the Gauss map of higher order for space curves. (English) Zbl 0752.14032
Let \(X\) be a non-degenerate curve in the projective space \(\mathbb{P}^ N\) over an algebraically closed field of characteristic \(p>0\). The authors determine the inseparable degree of the Gauss map defined by the osculating \(m\)-planes of \(X\). More precisely, let \(x\) be a general point of \(X\), \(H\) a general hyperplane containing the osculating \(m\)-plane to \(X\) at \(x\), and \(b_{m+1}\) the intersection multiplicity of \(H\) and \(X\) in \(x\). Then the inseparable degree of the Gauss map of order \(m\) equals the highest power of \(p\) dividing \(b_{m+1}\).

MSC:
14H50 Plane and space curves
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