On nodal prime Fano threefolds of degree 10


We study the geometry and the period map of nodal complex prime Fano threefolds with index 1 and degree 10. We show that these threefolds are birationally isomorphic to Verra solids, i.e., hypersurfaces of bidegree (2, 2) in P × P. Using Verra’s results on the period map for these solids and on the Prym map for double étale covers of plane sextic curves, we… (More)