3861.pdf (288.36 kB)
Download file

Extremal rational elliptic threefolds

Download (288.36 kB)
journal contribution
posted on 13.07.2015, 12:52 by Artie PrendergastArtie Prendergast
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 Journal

Volume

59

Issue

3

Pages

535 - 572

Citation

PRENDERGAST-SMITH, A., 2010. Extremal rational elliptic threefolds. Michigan Mathematical Journal, 59 (3), pp. 535 - 572

Publisher

Mathematics Department, University of Michigan

Version

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

2010

Notes

This article was published in Michigan Mathematical Journal and is available here with the kind permission of the publisher..

ISSN

0026-2285

eISSN

1945-2365

Language

en

Usage metrics

Keywords

Exports