Birational rigidity of complete intersections

2015/07/01 by Fumiaki Suzuki, Suzuki, Fumiaki
Computer Science · Mathematics · #14E05 #14J45 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary: 14E08 #Secondary: 14B05

paper · pdf · doi:10.48550/arxiv.1507.00285

openalex publication_date 2015/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that every smooth complete intersection X defined by s hypersurfaces of degree d₁, ... , d_s in a projective space of dimension d₁ + ... + d_s is birationally superrigid if 5s +1 is at most 2(d₁ + ... + d_s + 1)/sqrtd₁...d_s. In particular, X is non-rational and Bir(X)=Aut(X). We also prove birational superrigidity of singular complete intersections with similar numerical condition. These extend the results proved by Tommaso de Fernex.

Related

• Birationally rigid hypersurfaces
• Birationally rigid complete intersections with a singular point of high\n multiplicity
• Birationally rigid Fano complete intersections. II
• Birationally rigid finite covers of the projective space
• Effective birational rigidity of Fano double hypersurfaces