We prove the main theorem on the structure of everywhere integral sections on a rational elliptic surface, which is formulated in the first part of the paper with the same title . A few examples are given to illustrate it, and some open questions in the case of higher arithmetic genus will be discussed.
"Gröbner basis, Mordell-Weil lattices and deformation of singularities, II." Proc. Japan Acad. Ser. A Math. Sci. 86 (2) 27 - 32, February 2010. https://doi.org/10.3792/pjaa.86.27