Cubic surfaces violating the Hasse principle are Zariski dense in the moduli scheme

2013/12/09 by Andreas-Stephan Elsenhans, Elsenhans, Andreas-Stephan, Jörg Jahnel +1
Mathematics · #14G05 #14J10 #14J26 #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Primary 11G35 #Secondary 14G25 #math.AG #math.NT #msc:11G35 #msc:14G05 #msc:14G25 #msc:14J10 #msc:14J26

paper · pdf · doi:10.48550/arxiv.1312.2572

arxiv created 2013/12/09 · openalex publication_date 2013/12/09 · arxiv updated 2013/12/10 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We construct new examples of cubic surfaces, for which the Hasse principle fails. Thereby, we show that, over every number field, the counterexamples to the Hasse principle are Zariski dense in the moduli scheme of non-singular cubic surfaces.

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