• Corpus ID: 238744336

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

  title={The geometry of three sections on certain rational elliptic surfaces and Mumford representations},
  author={Ryosuke Masuya},
  • R. Masuya
  • Published 13 October 2021
  • Mathematics
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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