English

Modular properties of nodal curves on K3 surfaces

Algebraic Geometry 2009-12-01 v1

Abstract

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.

Keywords

Cite

@article{arxiv.0911.5474,
  title  = {Modular properties of nodal curves on K3 surfaces},
  author = {Mihai Halic},
  journal= {arXiv preprint arXiv:0911.5474},
  year   = {2009}
}