Cheng GONG, Mina TEICHER, Meirav AMRAM, Wan-Yuan XU

Moduli spaces of arrangements of 11 projective lines with a quintuple point

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".

Anahtar Kelimeler:

Line arrangements, moduli spaces, irreducibility

Moduli spaces of arrangements of 11 projective lines with a quintuple point

Keywords:

Line arrangements, moduli spaces, irreducibility,

PDF

___

l] Amram M, Cohen M, Teicher M, Ye F. Moduli spaces of ten-line arrangements with double and triple points. arXiv:1306.6105v1.
Amram M, Teicher M, Ye F. Moduli spaces of arrangements of 10 projective lines with quadruple points. Adv Appl Math 2013; 3: 392—418.
Cohen DC, Suciu Al. The braid monodromy of plane algebraic curves and hyperplane arrangements. Comment Math Helv 1997; 72: 285—315.
Fan K. Direct product of free groups as the fundamental group of the complement of a union of lines. Michigan Math J 1997; 44: 283—291.
Randell R. Lattice-isotopic arrangements are topologically isomorphic. P Am Math Soc 1989; 107: 555—559.
Rybnikov G. On the fundamental group of the complement of a complex hyperplane arrangement. Funct Anal Appl
Wang S, Yau SST. Rigidity of differentiable structure for new class of line arrangements. Comm Anal Geom 2005; 13: 1057—1075.
Wang S, Yau SST. Diffeomorphic types of the complements of arrangements in (CPS, 1: Point arrangements. J Math
Soc Japan 2007; 59: 423—447.
Wang S, Yau SST. The diffeomorphic types of the complements of arrangements in (CPS, II. Sci China Ser A 2008; 51: 785802.
Yau SST, Ye F. Diffeomorphic types of complements of nice point arrangements in (ClP’1 . Sci China Ser A 2009; 52: 2774—2791.
Ye F. Classification of moduli spaces of arrangements of 9 projective lines. Pacific J Math 2013; 265: 243—256.