A note on gonality of curves on general hypersurfaces
Let \(X\subset \mathbb {P}^{n+1}\) be a very general hypersurface of degree \(d\geq 2n+2\). This note contains an annoucement on a strong theorem on the minimal gonality of a curve \(C\subset X\) passing through \(x\) (the covering gonality of \(X\)); with a few described exceptions it is \(d -\lfloor \frac{\sqrt{16n+1}-1}{2}\rfloor\). The paper contains a clear description of the relevant literature (also on the minimal genus of a curve contained in \(X\) and containing \(x\)).
scientific article; zbMATH DE number 6875288
scientific article