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 plane curves with interesting properties explicitly. As a result we are able to construct new examples...

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Bibliographic Details
Published in:arXiv.org 2021-03
Main Authors: Bannai, S, Kawana, N, Masuya, R, Tokunaga, H
Format: Article
Language:English
Subjects:
Curves
Online Access:Get full text
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Summary: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 plane curves with interesting properties explicitly. As a result we are able to construct new examples of Zariski pairs. Especially, we show the existence of a family of Zariski pairs that degenerate to the same conic-line arrangement.
ISSN:2331-8422