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.
From: Lisa Marquand [view email]
[v1]
Fri, 26 Jul 2024 17:57:12 UTC (39 KB)
[v2]
Fri, 2 Aug 2024 17:34:10 UTC (141 KB)
[v3]
Mon, 8 Sep 2025 22:55:22 UTC (162 KB)
[v4]
Thu, 25 Jun 2026 09:54:56 UTC (192 KB)
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