Global sections of twisted normal bundles of K3 surfaces and their hyperplane sections

Abstract

Let S⊂Pg be a smooth K3 surface of degree 2g−2, g≥3. We classify all the cases for which h0(NS/Pg(−2))≠0 and the cases for which h0(NS/Pg(−2))<h0(NC/Pg−1(−2)) for C⊂Pg−1 a general canonical curve section of S.