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February 2010 Gröbner basis, Mordell-Weil lattices and deformation of singularities, I
Tetsuji Shioda
Proc. Japan Acad. Ser. A Math. Sci. 86(2): 21-26 (February 2010). DOI: 10.3792/pjaa.86.21

Abstract

We 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.

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Tetsuji Shioda. "Gröbner basis, Mordell-Weil lattices and deformation of singularities, I." Proc. Japan Acad. Ser. A Math. Sci. 86 (2) 21 - 26, February 2010. https://doi.org/10.3792/pjaa.86.21

Information

Published: February 2010
First available in Project Euclid: 1 February 2010

zbMATH: 0895.16020
MathSciNet: MR2590185
Digital Object Identifier: 10.3792/pjaa.86.21

Subjects:
Primary: 11G05 , 14J26 , 14J27

Keywords: deformation of singularities , Gröbner basis , integral section , Mordell-Weil lattice

Rights: Copyright © 2010 The Japan Academy

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Vol.86 • No. 2 • February 2010
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