2-spanned surfaces of sectional genus six
Let \(L\) be a \(k\)-spanned line bundle on a complex projective smooth surface \(S\). This essentially means that the global sections of \(L\) separate suitable 0-cycles of length \(k + 1\) on \(S\). The precise definition and an extensive study can be found in a paper by \textit{M. Beltrametti} and \textit{A. J. Sommese} [cf. Algebraic Geometry, Proc. Int. Conf., L'Aquila 1988, Lect. Notes Math. 1417, 24-51 (1990; Zbl 0706.14007)]; there the pairs \((S,L)\) with \(k > 1\) and \(g(L) < 6\) are classified. -- In the paper under review the cases \(g(L) = 6\) and \(g(L) = 7\), \(k = 3\) are considered. As corollaries the author points out the pairs \((S,L)\) with \(L\) 2-spanned (3-spanned respectively) and degree \(< 11\) and (\(<13\) respectively). The main difficulty to overcome is to make any admissible list effective, i.e. to decide whether for some possible pair \((S,L)\), \(L\) is actually \(k\)-spanned.
scientific article; zbMATH DE number 590106
scientific article