On 4-generated bundles and directly linked subcanonical curves
Two curves \(\Gamma\), \(\Gamma\) ' in the complex projective space \({\mathbb{P}}^ 3\) are said to be directly linked if \(\Gamma\) \(\cup \Gamma '\) is the complete intersection of two surfaces. (This makes sense even if the curves are non-reduced or have a common component.) The author considers the case where \(\Gamma\) and \(\Gamma\) ' are both subcanonical in the sense that their canonical classes extend to line bundles on \({\mathbb{P}}^ 3\), or equivalently that they are the 0-loci of sections of rank-2 bundles E and E' on \({\mathbb{P}}^ 3\). He shows that E is then 4- generated in the sense that there is a surjection \(\oplus^{4}{\mathcal O}(- a_ i)\to E.\quad (The\) general bundle is 5-generated.) Moreover, although this surjection is not unique, the numbers \(a_ i\) are determined; it follows, that for a given subcanonical curve \(\Gamma\), there are at most three possibilities for the numerical characters of \(\Gamma\) '.
numerical characters of subcanonical curve
scientific article; zbMATH DE number 3964047