Trisections on Certain Rational Elliptic Surfaces and Families of Zariski Pairs Degenerating to the same Conic-line Arrangement

Abstract

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.