Rational curves on smooth hypersurfaces of low degree

Tim D Browning, Pankaj Vishe

Research output: Contribution to journalArticle (Academic Journal)peer-review

20 Citations (Scopus)
311 Downloads (Pure)


We establish the dimension and irreducibility of the moduli space of rational curves (of fixed degree) on arbitrary smooth hypersurfaces of sufficiently low degree. A spreading out argument reduces the problem to hypersurfaces defined over finite fields of large cardinality, which can then be tackled using a function field version of the Hardy-Littlewood circle method, in which particular care is taken to ensure uniformity in the size of the underlying finite field.
Original languageEnglish
Pages (from-to)1657–1675
Number of pages19
JournalAlgebra and Number Theory
Issue number7
Early online date7 Sept 2017
Publication statusPublished - Sept 2017


  • math.AG
  • math.NT
  • 14H10 (11P55, 14G05)


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