In this paper, we try to classify moduli spaces of arrangements of 11 lines with quintuple points. We show that moduli spaces of arrangements of 11 lines with quintuple points can consist of more than 2 connected components. | Turk J Math (2015) 39: 618 – 644 ¨ ITAK ˙ c TUB ⃝ Turkish Journal of Mathematics doi: Research Article Moduli spaces of arrangements of 11 projective lines with a quintuple point 1 Meirav AMRAM1,3 , Cheng GONG1,2 , Mina TEICHER2 , Wan-Yuan XU1,∗ Emmy Noether Research Institute for Mathematics, Bar-Ilan University, Ramat-Gan, Israel 2 School of Mathematics Sciences, Soochow University, Suzhou, Jiangsu, . China 3 Shamoon College of Engineering, Beer-Sheva, Israel Received: • Accepted/Published Online: • Printed: Abstract: In this paper, we try to classify moduli spaces of arrangements of 11 lines with quintuple points. We show that moduli spaces of arrangements of 11 lines with quintuple points can consist of more than 2 connected components. We also present defining equations of the arrangements whose moduli spaces are not irreducible after taking quotients by the complex conjugation by Maple and supply some “potential Zariski pairs”. Key words: Line arrangements, moduli spaces, irreducibility 1. Introduction Let A = {H1 , H2 , . . . , Hn } be a line arrangement in the complex projective plane CP2 , and denote by M (A) the corresponding complement of the arrangement. An essential topic in hyperplane arrangement theory is to study the intersection between topology of complements and combinatorics of intersection lattices. It is important to study how closely topology and combinatorics of a given arrangement are related. For line arrangements, Jiang and Yau [8] showed that homeomorphism of the complement always implies lattice isomorphism. However, the converse is not true in general for line arrangements. In [7] and [12], the authors found a large class of line arrangements whose intersection lattices determine topology of the complements, called nice arrangements and simple arrangements respectively. The notion of nice line arrangements has been generalized to .
