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arXiv · 2511.07545

Unirationality of hypersurfaces via highly tangent lines

Raymond Cheng
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Abstract

This article describes a unirationality construction for general low degree complete intersections in projective space which is based on a variety of highly tangent lines. Applied to hypersurfaces, this implies that a general hypersurface of degree $d \geq 6$ in projective $n$-space is unirational as soon as $n \geq 2^{(d-1)2^{d-5}}$, significantly improving classical bounds.

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Raymond Cheng. 2025-11-10. Unirationality of hypersurfaces via highly tangent lines. https://arxiv.org/abs/2511.07545

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