Geometry of Hypersurfaces with Isolated Singularities

2025/03/10 by Jiayi Hu, Hu, Jiayi, Fengyang Wang +2
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2503.07844

openalex publication_date 2025/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Σ of lines passing through a singular point y on a hypersurface Y ⊂ ℙⁿ. 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.

Related

• The standard conjectures for the variety of lines on a cubic hypersurface
• Lines, conics, and all that
• Birational rigidity of singular Fano hypersurfaces
• Singularities of Fano varieties of lines on singular cubic fourfolds
• The Fano variety of lines and rationality problem for a cubic hypersurface