# The geometry of three sections on certain rational elliptic surfaces and Mumford representations

@inproceedings{Masuya2021TheGO, title={The geometry of three sections on certain rational elliptic surfaces and Mumford representations}, author={Ryosuke Masuya}, year={2021} }

Let φ : S → C be an elliptic surface over a smooth projective curve C satisfying the conditions as follows: (i) φ is relatively minimal, (ii) φ has a section O : C → S and, (iii) φ has at least one singular fiber. Under these conditions, the Néron-Severi group NS(S) of S is finitely generated and torsion-free by [12, Theorem 1.2]. The base field of this article is always the field of complex numbers C. Let ES be the generic fiber of φ. ES can be regarded as a curve of genus 1 defined over the…

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