A Lefschetz type result for Koszul cohomology (Q1882572)

\textit{C. Voisin} [J. Eur. Math. Soc. (JEMS) 4, 363--404 (2002; Zbl 1080.14525)] not only solved in the even genus case Green's conjecture on the minimal free resolution of the canonical embedding of a general curve, but also gave a very powerful tool for proving similar results. She considered curves embedded in a \(K3\) surfaces and used Koszul cohomology. Her method was used and refined by several authors (e.g. \textit{M. Aprodu} [Math. Z. 241, No. 1, 1--15 (2002; Zbl 1037.14012); Math. Z. 243, No. 4, 775--778 (2003; Zbl 1071.14032)] and \textit{M. Teixidor i Bigas} [Duke Math. J. 111, No. 2, 195--222 (2002; Zbl 1059.14039)]). In the paper under review the authors give a general framework for this types of proofs, proving very strong results concerning the behaviour of Koszul cohomology under the restriction to a divisor.