Rational curves on elliptic surfaces

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4 Scopus citations


We prove that a very general elliptic surface E → P1 over the complex numbers with a section and with geometric genus pg ≥ 2 contains no rational curves other than the section and components of singular fibers. Equivalently, if E/C(t) is a very general elliptic curve of height d ≥ 3 and if L is a finite extension of C(t) with L ∼= C(u), then the Mordell-Weil group E(L) = 0.

Original languageEnglish (US)
Pages (from-to)357-377
Number of pages21
JournalJournal of Algebraic Geometry
Issue number2
StatePublished - 2017

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology


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