The Hasse Principle for Lines on del Pezzo Surfaces

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Jörg Jahnel
  • Daniel Loughran

Research Organisations

External Research Organisations

  • University of Siegen
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Details

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

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.

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Cite this

The Hasse Principle for Lines on del Pezzo Surfaces. / Jahnel, Jörg; Loughran, Daniel.
In: International Mathematics Research Notices, Vol. 2015, No. 23, 2015, p. 12877-12919.

Research output: Contribution to journal › Article › Research › peer review

Jahnel J, Loughran D. The Hasse Principle for Lines on del Pezzo Surfaces. International Mathematics Research Notices. 2015;2015(23):12877-12919. doi: 10.1093/imrn/rnv073
Jahnel, Jörg ; Loughran, Daniel. / The Hasse Principle for Lines on del Pezzo Surfaces. In: International Mathematics Research Notices. 2015 ; Vol. 2015, No. 23. pp. 12877-12919.
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