On the vanishing of higher syzygies of curves. II (Q1395397)

The author verifies \textit{M. Green}'s conjecture [J. Differ. Geom. 19, 125--167, 168--171 (1984; Zbl 0559.14008)] in the case of small gonality; namely, for a generic \(k\)-gonal curve of genus \(g\) such that \(g\geq k(k-1)\). In this situation, the proof can be carried out relatively simple by computing the Koszul cohomology of a Hirzebruch surface, and relating it to the Koszul cohomology of strict transforms of nodal curves. Using different methods, \textit{M. Teixidor i Bigas} [Duke Math. J. 111, No. 2, 195--222 (2002; Zbl 1059.14039)] proved a stronger result. \textit{C. Voisin} [J. Eur. Math. Soc. (JEMS) 4, 363--404 (2002; Zbl 1080.14525)] provided powerful tools for the general case (and used it to prove the even genus case for a canonical embedding).