Classification of moduli spaces of arrangements of nine projective lines

Fei Ye

Vol. 265 (2013), No. 1, 243–256

DOI: 10.2140/pjm.2013.265.243

Abstract

In the study of line arrangements, searching for minimal examples of line arrangements whose fundamental groups are not combinatorially invariant is a very interesting and hard problem. It is known that such a minimal arrangement must have at least 9 lines. In this paper, we extend the number to 10 by a new method. We classify arrangements of 9 projective lines according to the irreducibility of their moduli spaces and show that fundamental groups of complements of arrangements of 9 projective lines are combinatorially invariant. The idea and results have been used to classify arrangements of 10 projective lines.

Keywords

line arrangements, moduli spaces

Mathematical Subject Classification 2010

Primary: 14N20, 32S22, 52C35

Milestones

Received: 3 July 2012

Revised: 13 November 2012

Accepted: 11 February 2013

Published: 28 August 2013