Quartic del Pezzo surfaces over function fields of curves

Brendan Hassett, Yuri Tschinkel

Research output: Contribution to journalArticle

Abstract

We classify quartic del Pezzo surface fibrations over the projective line via numerical invariants, giving explicit examples for small values of the invariants. For generic such fibrations, we describe explicitly the geometry of spaces of sections to the fibration, and mappings to the intermediate Jacobian of the total space. We exhibit examples where these are birational, which has applications to arithmetic questions, especially over finite fields.

Original languageEnglish (US)
Pages (from-to)395-420
Number of pages26
JournalCentral European Journal of Mathematics
Volume12
Issue number3
DOIs
StatePublished - 2014

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Del Pezzo Surfaces
Fibration
Function Fields
Quartic
Curve
Invariant
Galois field
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Line

Keywords

  • Del Pezzo surfaces
  • Fibrations
  • Function fields of curves
  • Intermediate Jacobians
  • Rational points

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Quartic del Pezzo surfaces over function fields of curves. / Hassett, Brendan; Tschinkel, Yuri.

In: Central European Journal of Mathematics, Vol. 12, No. 3, 2014, p. 395-420.

Research output: Contribution to journalArticle

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