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

Abstract

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

Deformations and extensions of Gorenstein weighted projective spaces

“…By Proposition 6.1, P ⊂ P g+1 has the property N 2 , hence H 0 (N P/P g+1 (−2)) = 0 (see [Kn,Lem. 1.1] and the references therein).…”

“…The possibilities for the pair (S, L 1 ) and j are then very limited. In particular, H 0 (S, N S/P g (−j)) = 0 for all j ≥ 2 as soon as S satisfies the property N 2 (see Definition 4.7), see [Kn,Lem. 1.1] and the references therein.…”