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Corpus ID: 239049373

Linear subspaces of minimal codimension in hypersurfaces

@inproceedings{Kazhdan2021LinearSO,
title={Linear subspaces of minimal codimension in hypersurfaces},
author={David Kazhdan and Alexander Polishchuk},
year={2021}
}

Let k be a perfect field and let X ⊂ P be a hypersurface of degree d defined over k and containing a linear subspace L defined over k with codim PN L = r. We show that X contains a linear subspace L0 defined over k with codim PN L ≤ dr. We conjecture that the intersection of all linear subspaces (over k) of minimal codimension r contained in X, has codimension bounded above only in terms of r and d. We prove this when either d ≤ 3 or r ≤ 2.

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