Birational geometry of Fano varieties of lines on cubic fourfolds containing pairs of cubic scrolls

Abstract

We characterize the birational geometry of some hyperkahler fourfolds of Picard rank 3 obtained as the Fano varieties of lines on cubic fourfolds containing pairs of cubic scrolls. In each of the two cases considered, we provide a census of the birational models, relating each model to familiar geometric constructions. We also provide structural results about the birational automorphism groups, giving generators in both cases and a full set of relations in one case. Finally, as a byproduct of our analysis, we obtain non-isomorphic cubic fourfolds whose Fano varieties of lines are birationally equivalent.

Publication Details

Preprint: arXiv:2407.18904 (2024)
Citations: 1 (as of 2024)