The Wahl map of one-nodal curves on K3 surfaces

Abstract

We consider a general primitively polarized K3 surface $(S,H)$ of genus $g+1$ and a 1-nodal curve $\tilde{C}\in |H|$. We prove that the normalization $C$ of $\tilde{C}$ has surjective Wahl map provided $g=40,42$ or $\ge 44$.

arXiv comment9 pages. Final version, to appear in Contemporary Mathematics. Same results as in v1, new proof of Lemma 3, minor changes in section 1, typos corrected