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Dimensions of Fano schemes of lines on hypersurfaces
Abstract
Let X⊂ℙnC be a smooth hypersurface of degree d≥2, with n≥3. We prove that an m-dimensional integral projective family of lines sweeping a variety of dimension y satisfies m≤max{2y−d−1,n−3}. This proves the de Jong-Debarre conjecture for d≤ n and the Beheshti-Starr bound for lines on smooth hypersurfaces for d≥ n+1.
Related
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BibTeX
@misc{yu2026dimensions,
title = {{Dimensions of Fano schemes of lines on hypersurfaces}},
author = {Chenglong Yu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38812},
eprint = {2610.38812},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38812},
}
RIS
TY - UNPB
TI - Dimensions of Fano schemes of lines on hypersurfaces
AU - Chenglong Yu
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38812
UR - https://arxiv.org/abs/2610.38812
AB - Let X⊂ℙ^n_C be a smooth hypersurface of degree d≥2, with n≥3. We prove that an m-dimensional integral projective family of lines sweeping a variety of dimension y satisfies m≤max{2y−d−1,n−3}. This proves the de Jong-Debarre conjecture for d≤ n and the Beheshti-Starr bound for lines on smooth hypersurfaces for d≥ n+1.
ER -