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On the number of points determining a canonical curve. (English) Zbl 0724.14017
The author shows, among other things, that a canonical curve of genus \(g\) passes through \(g+5\) points of \({\mathbb{P}}^{g-1}\). The proof is based on work of Kleppe [via D. Perrin, Mém. Soc. Math. Fr., Nouv. Ser. 28/29, (1987; Zbl 0648.14028)]. One application is to study the singularity given by r general lines through a point in \({\mathbb{A}}^ n\), with \(n<r<{{n+1}\choose 2}:\) if \(r-n\neq 8\), this singularity is smoothable exactly when \((r-n-2)(n-5)\leq 6\epsilon\), where \(\epsilon =0\) or 1 according to the parity of \(r-n\).
Reviewer: R.Speiser (Provo)

14H50 Plane and space curves
14H20 Singularities of curves, local rings
14N10 Enumerative problems (combinatorial problems) in algebraic geometry