On one stable birational invariant

2013/07/22 by Ilya Karzhemanov, Karzhemanov, Ilya
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1307.5605

Proof of Lemma 2.2 fixed

openalex publication_date 2013/07/22 · arxiv created 2013/09/15 · arxiv updated 2013/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is an expository article, which contributes to the Proceedings of the conference "Groups of Automorphisms in Birational and Affine Geometry", held in Trento in 2012. We propose that (rational) fibrations on the projective space \pⁿ by (birationally) Abelian hypersurfaces, for an arbitrary n≥ 2, provide an obstruction to stable rationality of algebraic varieties. We discuss the evidence for this proposition and derive some (almost straightforward) corollaries from it.

Citations

• Good Reduction of Abelian Varieties

Related

• Bounded birationality and isomorphism problems are computable
• Unboundedness for motivic invariants of birational automorphisms
• Complexes of stable birational invariants
• Birational geometry of algebraic varieties, fibred into Fano double\n spaces
• Variation of Stable Birational Types of Hypersurfaces