Rational curves on smooth hypersurfaces of low degree

Tim D Browning, Pankaj Vishe

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

8 Citations (Scopus)
262 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 Sep 2017
Publication statusPublished - Sep 2017


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

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