• Corpus ID: 238744336

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}
}
  • 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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References

SHOWING 1-10 OF 19 REFERENCES
Trisections on Certain Rational Elliptic Surfaces and Families of Zariski Pairs Degenerating to the same Conic-line Arrangement
In this paper, we study the geometry of trisections on certain rational elliptic surfaces. We utilize Mumford representations of semi-reduced divisors in order to construct trisections and related
Sections of elliptic surfaces and Zariski pairs for conic-line arrangements via dihedral covers
In this article, we make use of geometry of sections of elliptic surfaces and elementary arithmetic on the Mordell-Weil group in order to study existence problem of dihedral covers with given reduced
Theta-characteristics on algebraic curves
The theory of theta-characteristics is developed algebraically, so that it may be applied to possibly singular and/or reducible algebraic curves. The configuration of theta-characteristics on a curve
Geometry of bisections of elliptic surfaces and Zariski N-plets II
Abstract In this article, we consider Zariski N-plets whose irreducible components are an irreducible quartic and smooth conics. More precisely we give examples of Zariski N + 1 -plets of degree 2 N
Compact complex surfaces.
Historical Note.- References.- The Content of the Book.- Standard Notations.- I. Preliminaries.- Topology and Algebra.- 1. Notations and Basic Facts.- 2. Some Properties of Bilinear forms.- 3. Vector
Representations of divisors on hyperelliptic curves, Gr\"obner bases and plane curves with quasi-toric relations
In the study of hyperelliptic curve cryptography, presentations of semi-reduced divisors on a hyperelliptic curve play important roles. In this note, we give an interpretation for such presentations
Geometry of irreducible plane quartics and their quadratic residue conics
Let $D$ be an irreducible plane curve. In this article, we first introduce a notion of a quadratic residue curve mod $D$, and study quadratic residue concis $C$ mod an irreducible quartic curve $Q$.
Geometry of bisections of elliptic surfaces and Zariski $$N$$N-plets for conic arrangements
In this article, we study the geometry of bisections of certain rational elliptic surfaces. As an application, we give examples of Zariski $$N$$N-plets for conic arrangements, which generalize
Mordell–Weil Lattices
In this chapter, we give the definition of Mordell–Weil lattice (in Sect. 6.5). First, we bring together the concepts from Chaps. 4 and 5 in order to gain a better understanding of the Neron–Severi
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