Non-rationality of the S₆-symmetric quartic threefolds

2012/12/21 by Arnaud Beauville, Beauville, Arnaud
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #math.AG

paper · pdf · doi:10.48550/arxiv.1212.5345

One (annoying) typo corrected

openalex publication_date 2012/12/21 · arxiv created 2013/01/02 · arxiv updated 2013/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The quartic hypersurfaces in P⁴ invariant under the standard representation of S₆ form a linear pencil. We prove that a general member of this pencil is not rational.

Related

• Rationality of an S₆-invariant quartic 3-fold
• A very general quartic double fourfold or fivefold is not stably rational
• A very general quartic double fourfold is not stably rational
• Hypersurfaces that are not stably rational
• The diagonal of quartic fivefolds