Stably irrational hypersurfaces of small slopes

2018/01/31 by Stefan Schreieder · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Algebraic number #Degree (music) #Dimension (graph theory) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Hypersurface #Irrational number #Uncountable set #Upper and lower bounds #math.AG #math.CV #msc:14C30 #msc:14E08 #msc:14J70 #msc:14M20

paper · pdf · doi:10.1090/jams/928

published as J. Amer. Math. Soc. 32 (2019), 1171-1199 · 34 pages; Appendix with explicit equations added. To appear in Journal of the AMS

openalex created_date 2018/01/26 · openalex publication_date 2019/06/28 · arxiv created 2019/10/21 · arxiv updated 2019/10/23 · openalex updated_date 2026/08/05

Abstract

Let k be an uncountable field of characteristic different from two. We show that a very general hypersurface of dimension N>2 and degree at least log₂N +2 is not stably rational over the algebraic closure of k.

Citations

• Rational Curves on Algebraic Varieties
• Some Elementary Examples of Unirational Varieties Which are Not Rational
• Motivic cohomology with 𝐙 / 2 -coefficients
• THREE-DIMENSIONAL QUARTICS AND COUNTEREXAMPLES TO THE LÜROTH PROBLEM
• Cohomologie non ramifiée et conjecture de Hodge entière
• Smoothness, semi-stability and alterations
• Stable rationality of quadric surface bundles over surfaces
• The Intermediate Jacobian of the Cubic Threefold
• Intersection Theory

Cited by

• Rational variety [wikipedia]

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