Moduli spaces of arrangements of 12 projective lines with a sextic point

Abstract

*This paper is from 2018* In this paper, we try to classify moduli spaces of arrangements of $12$ lines with sextic points. We show that moduli spaces of arrangements of $12$ lines with sextic points can consist of more than two connected components. We also present defining equations of the arrangements whose moduli spaces are not irreducible taking quotients by the complex conjugation by supply some potential Zariski pairs. Through complex conjugation we take quotients and supply some potential Zariski pairs.