Separable rational connectedness and $k$-plane sections of hypersurfaces

Roya Beheshti; Shibashis Mukhopadhyay; Eric Riedl

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arXiv · 2512.15903

Separable rational connectedness and $k$-plane sections of hypersurfaces

Roya Beheshti·Shibashis Mukhopadhyay·Eric Riedl

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Abstract

Let X be a smooth hypersurface of degree d in P^n over an algebraically closed field of characteristic p. We show that X must be separably rationally connected and must contain a free line if either p is at least d or if p is at least d-1 and the defining equation has some partial derivative that is not too singular. We also show that X must be separably rationally connected in any characteristic if d = 4 and n is sufficiently large. Along the way, we generalize results on the spaces of k-planes in X to characteristic p and connect some of these questions to the spaces of linear sections of X.

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BibTeX RIS

Roya Beheshti, Shibashis Mukhopadhyay, Eric Riedl. 2025-12-17. Separable rational connectedness and $k$-plane sections of hypersurfaces. https://arxiv.org/abs/2512.15903

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