Vector bundles on Fano varieties of genus ten

In this note we describe a unique linear embedding of a prime Fano 4-fold of genus 10 into the Grassmannian . We use this to construct some moduli spaces of bundles on linear sections of . In particular the moduli space of bundles with Mukai vector on a generic polarized K3 surface of genus 10 is constructed as a double cover of branched over a smooth sextic.