A characterization of bielliptic curves via syzygy schemes (Q2001418)

Let \(C\subset \mathbb {P}^{g-1}\) the canonical model of a smooth genus \(g\) curves. If \(g\ge 11\) the authors shows that the second syzygy scheme of \(C\) is \(\ne C\) if and only if \(C\) is a bielliptic curve. For lower \(g\) they classify the second syzygy scheme of the \(4\)-gonal curves. For the proof they first exclude the curves with Clifford index \(\ge 3\) and then analize the \(4\)-gonal curves.