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arXiv · 2503.07844

Geometry of Hypersurfaces with Isolated Singularities

Jiayi Hu·Fengyang Wang·Xinlang Zhu
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Abstract

This paper explores the Fano variety of lines in hypersurfaces, particularly focusing on those with mild singularities. Our first result explores the irreducibility of the variety $\Sigma$ of lines passing through a singular point $y$ on a hypersurface $Y \subset \mathbb{P}^n$. Our second result studies the Fano variety of lines of cubic hypersurfaces with more than one singular point, motivated by Voisin's construction of a dominant rational self map.

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Jiayi Hu, Fengyang Wang, Xinlang Zhu. 2025-03-10. Geometry of Hypersurfaces with Isolated Singularities. https://arxiv.org/abs/2503.07844

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