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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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