2023/05/25 by Александр Валентинович Пухликов, Pukhlikov, Aleksandr V.
Mathematics · #14E05 #14E07 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2305.16219
openalex publication_date 2023/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we prove the birational rigidity of Fano-Mori fibre spaces π\colon V→ S, every fibre of which is a Fano complete intersection of index 1 and codimension k\geqslant 3 in the projective space \mathbb PM+k for M sufficiently high, satisfying certain natural conditions of general position, in the assumption that the fibre space V/S is sufficiently twisted over the base. The dimension of the base S is bounded from above by a constant, depending only on the dimension M of the fibre (as the dimension of the fibre M grows, this constant grows as \frac12 M2).