Rank Two Sheaves on K3 Surfaces: A Special Construction

الأصل · EN

Let X be a K3 surface of degree 8 in P⁵ with hyperplane section H. We associate to it another K3 surface M which is a double cover of P² 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 c₁=H and c₂=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.