Rank Two Sheaves on K3 Surfaces: A Special Construction
Algebraic Geometry
2014-01-08 v3
Abstract
Let X be a K3 surface of degree 8 in P^5 with hyperplane section H. We associate to it another K3 surface M which is a double cover of P^2 ramified on a sextic curve C. In the generic case when X is smooth and a complete intersection of three quadrics, there is a natural correspondence between M and the moduli space M' of rank two vector bundles on X with Chern classes c_1=H and c_2=4. We build on previous work of Mukai and others, giving conditions and examples where M' is fine, compact, non-empty; and birational or isomorphic to M. We also present an explicit calculation of the Fourier-Mukai transform when X contains a line and has Picard number two.
Cite
@article{arxiv.0803.0179,
title = {Rank Two Sheaves on K3 Surfaces: A Special Construction},
author = {Colin Ingalls and Madeeha Khalid},
journal= {arXiv preprint arXiv:0803.0179},
year = {2014}
}
Comments
Fixed various minor errors and reworked some arguments