Nodal curves with general moduli on K3 surfaces
Algebraic Geometry
2007-07-03 v1
Abstract
We investigate the modular properties of nodal curves on a low genus K3 surface. We prove that a general genus g curve C is the normalization of a d-nodal curve X sitting on a primitively polarized K3 surface S of degree 2p-2, for p any integer between 3 and 11 and g = p - d between 2 and p. The proof is based on a local deformation-theoretic analysis of the map from the stack of pairs (S,X) to the moduli space of curves of genus g that associates to X the isomorphism class [C] of its normalization.
Cite
@article{arxiv.0707.0157,
title = {Nodal curves with general moduli on K3 surfaces},
author = {Flaminio Flamini and Andreas L. Knutsen and Gianluca Pacienza and Edoardo Sernesi},
journal= {arXiv preprint arXiv:0707.0157},
year = {2007}
}
Comments
12 pages. Submitted preprint