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Title: | Extremal rational elliptic threefolds |
Authors: | Prendergast-Smith, Artie |
Issue Date: | 2010 |
Publisher: | Mathematics Department, University of Michigan |
Citation: | PRENDERGAST-SMITH, A., 2010. Extremal rational elliptic threefolds. Michigan Mathematical Journal, 59 (3), pp. 535 - 572 |
Abstract: | 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. |
Description: | This article was published in Michigan Mathematical Journal and is available here with the kind permission of the publisher.. |
Version: | Published |
DOI: | 10.1307/mmj/1291213956 |
URI: | https://dspace.lboro.ac.uk/2134/18238 |
Publisher Link: | http://dx.doi.org/10.1307/mmj/1291213956 |
ISSN: | 0026-2285 |
Appears in Collections: | Published Articles (Maths)
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