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TitleGr\"obner basis, Mordell-Weil lattices and deformation of singularities. I.
Author(s) Tetsuji Shioda
TypeArticle in Journal
AbstractWe call a section of an elliptic surface to be everywhere integral if it is disjoint from the zero-section. The set of everywhere integral sections of an elliptic surface is a finite set under a mild condition. We pose the basic problem about this set when the base curve is P1. In the case of a rational elliptic surface, we obtain a complete answer, described in terms of the root lattice E8 and its roots. Our results are related to some problems in Gröbner basis, Mordell-Weil lattices and deformation of singularities, which have served as the motivation and idea of proof as well.
ISSN0386-2194
URL http://projecteuclid.org/euclid.pja/1265033217
LanguageEnglish
JournalProc. Japan Acad., Ser. A
Volume86
Number2
Pages21--26
PublisherJapan Academy, Ueno Park, Tokyo
Year2010
Edition0
Translation No
Refereed No
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