Abstract
In this article we are going to address the following issues: (1) the first is a rigidity property for pairs (S, C) consisting of a general projective K3 surface S, and a curve C obtained as the normalization of a nodal, hyperplane section \({\hat C\hookrightarrow S}\). We prove that a non-trivial deformation of a pair (S, C) induces a non-trivial deformation of C; (2) the second question concerns the Wahl map of curves C obtained as above. We prove that the Wahl map of the normalization of a nodal curve contained in a general projective K3 surface is non-surjective. In both cases, we impose upper bounds on the number of nodes of \({\hat C}\).
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