Intersections of three quadrics in ℙ⁷

2017/06/05 by Brendan Hassett, Alena Pirutka, Hassett, Brendan +3
Computer Science · Mathematics · #14C30 #14E08 #14F20 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14C30 #msc:14E08 #msc:14F20

paper · pdf · doi:10.48550/arxiv.1706.01371

18 pages

arxiv created 2017/06/05 · openalex publication_date 2017/06/05 · arxiv updated 2017/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study rationality properties of smooth complete intersections of three quadrics in ℙ⁷. We exhibit a smooth family of such intersections with both rational and non-rational fibers.

Citations

• Quadric surface bundles over surfaces
• Stable rationality of quadric surface bundles over surfaces

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• Varieties of planes on intersections of three quadrics
• Rationality of even-dimensional intersections of two real quadrics
• The intersection of three quadrics in P⁷ revisited
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