Birational geometry of Fano varieties of lines on cubic fourfolds containing pairs of cubic scrolls
Abstract
We characterize the birational geometry of some hyperkähler 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:
-
arXiv e-prints
- Pub Date:
- July 2024
- DOI:
- 10.48550/arXiv.2407.18904
- arXiv:
- arXiv:2407.18904
- Bibcode:
- 2024arXiv240718904B
- Keywords:
-
- Mathematics - Algebraic Geometry;
- 14J42;
- 14E08;
- 14E07;
- 14J35
- E-Print:
- v2: updated figures and ancillary files. 34 pages, 4 figures, two ancillary files