O některých křivkách z kuželosečky odvozených
The minimal free resolution of the Hartshorne-Rao module of a curve with natural cohomology is studied, and conditions are given on the degrees and the ranks of the terms of this resolution.
The classical Segre theory gives a necessary and sufficient condition for a plane curve to be a branch curve of a (generic) projection of a smooth surface in . We generalize this result for smooth surfaces in a projective space of any dimension in the following way: given two plane curves, and , we give a necessary and sufficient condition for to be the branch curve of a surface in and to be the image of the double curve of a -model of . In the classical Segre theory, a plane curve...
Let C be a smooth curve of genus g. For each positive integer r the birational r-gonality sr(C) of C is the minimal integer t such that there is L ∈ Pict(C) with h0(C,L) = r + 1. Fix an integer r ≥ 3. In this paper we prove the existence of an integer gr such that for every integer g ≥ gr there is a smooth curve C of genus g with sr+1(C)/(r + 1) > sr(C)/r, i.e. in the sequence of all birational gonalities of C at least one of the slope inequalities fails