The Hasse Principle for Lines on del Pezzo Surfaces

Jörg Jahnel, Daniel Loughran

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2 Citations (Scopus)

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 pages33
JournalInternational Mathematics Research Notices
Volume2015
Issue number23
DOIs
Publication statusPublished - 27 Mar 2015

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