Birational rigidity is not an open property

2006/12/06 by Ivan Cheltsov, I. A. Cheltsov, Cheltsov, I. A. +3 · 1 citation
Chemistry · Mathematics · #14E05 #14E07 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Organometallic Complex Synthesis and Catalysis #math.AG #msc:14E05 #msc:14E07

paper · pdf · doi:10.48550/arxiv.math/0612159

26 pages

arxiv created 2006/12/06 · openalex publication_date 2006/12/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct an example of the birationally rigid complete intersection of a quadric and a cubic in \PA⁵ with an ordinary double point, which under a small deformation gives a non-rigid Fano variety. Thus we show that birational rigidity is not open in moduli.

Citations

• Q-factorial quartic threefolds

Cited by

• A survey on birational Rigidity of threefold Weighted Complete Intersections

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