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

2024/07/26 by Corey Brooke, Brooke, Corey, Sarah Frei +5 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2407.18904

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 identify all of the birational models, relating each model to familiar geometric constructions, and give explicit birational maps between them. 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.

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• Some remarks on L-equivalence for cubic fourfolds and hyper-Kähler manifolds

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