The Hasse Principle for Lines on del Pezzo Surfaces

Jörg Jahnel, Daniel Loughran

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    Abstract

    In this paper, we consider the following problem: Does there exist a cubic surface over Q which contains no line over Q, yet contains a line over every completion of Q? This question may be interpreted as asking whether the Hilbert scheme of lines on a cubic surface can fail the Hasse principle. We also consider analogous problems, over arbitrary number fields, for other del Pezzo surfaces and complete intersections of two quadrics.

    Original languageEnglish
    Pages (from-to)12877-12919
    Number of pages43
    JournalInternational Mathematics Research Notices
    Volume2015
    Issue number23
    DOIs
    Publication statusPublished - 27 Mar 2015

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