arXiv subjects
Publications and source records attributed to Hiro-O Tokunaga.
Let ${\mathcal {B}}$ be a reducible reduced plane curve. We introduce a new point of view to study the topology of $(\PP^2, {\mathcal {B}})$ via Galois covers and Alexander polynomials. We show its effectiveness through examples of Zariski $N$-plets for conic and conic-quartic configurations.
We study the Abel-Jacobi map for bisections of a certain rational elliptic surface. As an application, we construct examples of Zariski $N$-plets for conic arrangements.
In this article, examples of Zariski pairs $(B_1, B_2)$ satisfying the following condition are given: (i) $°B_1 = °B_2 = 7$. (ii) Irreducible components of $B_i$ $(i = 1, 2)$ are lines and conics. (iii) Singularities of $B_i$ $(i = 1, 2)$ are nodes, tacnodes and ordinary triple points. In order to construct $B_i$ ($i = 1, 2$), we make use of geometry of sections of rational elliptic surfaces and their group structure. Dihedral covers play important roles to distinguish the topology of $({\mathbb P}^2, B_i)$ $(i = 1, 2)$.