On the geometry of certain irreducible non-torus plane sextics

Kodai Mathematical Journal

Mutsuo Oka¹  Christophe Eyral² 

[1] Department of Mathematics Tokyo University of Science;Department of Mathematical Sciences University of Aarhus

关键词: Irreducible non-torus plane sextic;    Fundamental group;    Alexander-equivalent Zariski pair;   

DOI  :  10.2996/kmj/1257948886

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

References(22)An irreducible non-torus plane sextic with simple singularities is said to be special if its fundamental group factors to a dihedral group. There exist (exactly) ten configurations of simple singularities that are realizable by such curves. Among them, six are realizable by non-special sextics as well. We conjecture that for each of these six configurations there always exists a non-special curve whose fundamental group is abelian, and we prove this conjecture for three configurations (another one has already been treated in one of our previous papers). As a corollary, we obtain new explicit examples of Alexander-equivalent Zariski pairs of irreducible sextics.

【 授权许可】

Unknown