Trigonal hyperplane sections of projective surfaces
Let X be a smooth surface in \({\mathbb{P}}^ n\). Assume that at least one of the hyperplane sections, C, of X is a smooth r-gonal curve. Then it is a quite classical question to describe the pair (X,L) with \(L\cong {\mathcal O}_ X(C)\). - If \(r=2\) there is a complete description of surfaces containing at least one hyperelliptic hyperplane section. This is due to Serrano, Sommese and Sommese-Van de Ven. If \(r>2\) there are only partial results due to Serrano. In the paper the case \(r=3\) is completely worked out. The main tools are adjunction theory results and Reider's type results.
scientific article; zbMATH DE number 4204548
scientific article