Birational rigidity and K-stability of Fano hypersurfaces with ordinary double points

2021/11/18 by Tommaso de Fernex, de Fernex, Tommaso
Mathematics · #14E08 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Primary: 14J45 #Secondary: 32Q20

paper · pdf · doi:10.48550/arxiv.2111.09911

openalex publication_date 2021/11/18 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

Extending previous results, we prove that for n ≥ 5 all hypersurfaces of degree n+1 in \mathbb Pⁿ⁺¹ with isolated ordinary double points are birational superrigid and K-stable, hence admit a weak Kähler--Einstein metric.

Related

• Fano hypersurfaces and their birational geometry
• Birational rigidity of singular Fano hypersurfaces
• Birationally rigid hypersurfaces with quadratic singularities of low rank
• K-stability of birationally superrigid Fano 3-fold weighted hypersurfaces
• Effective birational rigidity of Fano double hypersurfaces