Lines on cubic threefolds and fourfolds containing a plane

2022/11/24 by Brooke, Corey · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.13444

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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• A note on cubic fourfolds containing several planes

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