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Extremal rational elliptic threefolds
An elliptic fibration is a proper morphism f : X → Y of normal projective varieties whose
generic fibre E is a regular curve of genus 1. The Mordell–Weil rank of such a fibration is
defined to be the rank of the finitely generated abelian group Pic0 E of degree-0 line bundles
on E. In particular, f is called extremal if its Mordell–Weil rank is 0.
The simplest nontrivial elliptic fibration is a rational elliptic surface f : X → P1. There
is a complete classification of extremal rational elliptic surfaces, due to Miranda–Persson
in characteristic 0 [14] and W. Lang in positive characteristic [12, 13]. (See also Cossec–
Dolgachev [4, Section 5.6].) The purpose of the present paper is to produce a corresponding
classification of a certain class of extremal rational elliptic threefolds.
History
School
- Science
Department
- Mathematical Sciences
Published in
Michigan Mathematical JournalVolume
59Issue
3Pages
535 - 572Citation
PRENDERGAST-SMITH, A., 2010. Extremal rational elliptic threefolds. Michigan Mathematical Journal, 59 (3), pp. 535 - 572Publisher
Mathematics Department, University of MichiganVersion
- VoR (Version of Record)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2010Notes
This article was published in Michigan Mathematical Journal and is available here with the kind permission of the publisher..ISSN
0026-2285eISSN
1945-2365Publisher version
Language
- en