Birational geometry of the Mukai system of rank two and genus two

Abstract

Using the techniques of Bayer–Macrì, we determine the walls in the movable cone of the Mukai system of rank two for a general K3 surface $S$ of genus two. We study the (essentially unique) birational map to $S^{[5]}$ and decompose it into a sequence of flops. We give an interpretation of the exceptional loci in terms of Brill–Noether loci.