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arXiv · 2211.13444

Lines on cubic threefolds and fourfolds containing a plane

Corey Brooke
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Abstract

We describe the Fano scheme of lines on a general cubic threefold containing a plane over a field $k$ of characteristic different from 2. Then, we use the Fano scheme to characterize rationality for such cubic threefolds over nonclosed fields and to construct a Lagrangian fibration from the Fano variety of lines on a cubic fourfold containing a plane explicitly.

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Corey Brooke. 2022-11-24. Lines on cubic threefolds and fourfolds containing a plane. https://arxiv.org/abs/2211.13444

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