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15 July 2021 Linear subspaces of hypersurfaces
Roya Beheshti, Eric Riedl
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Duke Math. J. 170(10): 2263-2288 (15 July 2021). DOI: 10.1215/00127094-2021-0035

Abstract

Let X be an arbitrary smooth hypersurface in CPn of degree d. We prove the de Jong–Debarre conjecture for n2d4: the space of lines in X has dimension 2nd3. We also prove an analogous result for k-planes: if n2d+k1k+k, then the space of k-planes on X will be irreducible of the expected dimension. As applications, we prove that an arbitrary smooth hypersurface satisfying n2d! is unirational, and we prove that the space of degree-e curves on X will be irreducible of the expected dimension provided that de+n e+1.

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Roya Beheshti. Eric Riedl. "Linear subspaces of hypersurfaces." Duke Math. J. 170 (10) 2263 - 2288, 15 July 2021. https://doi.org/10.1215/00127094-2021-0035

Information

Received: 9 September 2019; Revised: 11 September 2020; Published: 15 July 2021
First available in Project Euclid: 15 June 2021

Digital Object Identifier: 10.1215/00127094-2021-0035

Subjects:
Primary: 14E08
Secondary: 14H10

Rights: Copyright © 2021 Duke University Press

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Vol.170 • No. 10 • 15 July 2021
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