Everywhere local solubility for hypersurfaces in products of projective spaces

DOI10.1007/s40993-020-00223-zzbMath1468.11150arXiv1911.09623OpenAlexW3119037888MaRDI QIDQ2221693

Tom A. Fisher, Jennifer Park, Wei Ho

Publication date: 2 February 2021

Published in: Research in Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.09623

zbMATH Keywords

hypersurfacesHasse principle

Mathematics Subject Classification ID

Rational points (14G05) Quadratic forms over global rings and fields (11E12) Varieties over global fields (11G35) Fano varieties (14J45) Varieties over finite and local fields (11G25)

Related Items (2)

The proportion of genus one curves over ℚ defined by a binary quartic that everywhere locally have a point ⋮ On the proportion of locally soluble superelliptic curves

Uses Software

• Magma
• SageMath

Cites Work

• Manin's conjecture for certain biprojective hypersurfaces
• Coregular spaces and genus one curves
• Rational connectedness and boundedness of Fano manifolds
• The Magma algebra system. I: The user language
• Generalizing the Birch-Stephens theorem. I: Modular curves
• The Cassels-Tate pairing on polarized Abelian varieties
• Ample subvarieties of algebraic varieties. Notes written in collaboration with C. Musili
• The proportion of plane cubic curves over ℚ that everywhere locally have a point
• Failures of weak approximation in families
• Conditionally bounding analytic ranks of elliptic curves
• What is the Probability that a Random Integral Quadratic Form innVariables has an Integral Zero?
• Families of rationally connected varieties
• Some minimisation algorithms in arithmetic invariant theory
• Connexité rationnelle des variétés de Fano
• RATIONAL SURFACES WITH A PENCIL OF RATIONAL CURVES
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