Details:
Title  Gr\"obner basis, MordellWeil lattices and deformation of singularities. I.  Author(s)  Tetsuji Shioda  Type  Article in Journal  Abstract  We call a section of an elliptic surface to be everywhere integral if it is disjoint from the zerosection. 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, MordellWeil lattices and deformation of singularities, which have served as the motivation and idea of proof as well.  ISSN  03862194 
URL 
http://projecteuclid.org/euclid.pja/1265033217 
Language  English  Journal  Proc. Japan Acad., Ser. A  Volume  86  Number  2  Pages  2126  Publisher  Japan Academy, Ueno Park, Tokyo  Year  2010  Edition  0  Translation 
No  Refereed 
No 
