Modular properties of nodal curves on K3 surfaces

Details Modular properties of nodal curves on K3 surfaces Modular properties of nodal curves on K3 surfaces

2009-11-29

arxiv.org/abs/0911.5474v1

Mathematics

Algebraic Geometry

Scientific paper

In this paper we partially address two issues: - 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 of S. We prove that a non-trivial deformation of such a pair (S,C) induces a non-trivial deformation of C; - The second question concerns the Wahl map of curves C 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 the hyperplane section.

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