Real line arrangements with Hirzebruch property

Abstract

A line arrangement of $3n$ lines in $\mathbb{C}{P}^2$ satisfies Hirzebruch property if each line intersect others in $n+1$ points. Hirzebruch asked if all such arrangements are related to finite complex reflection groups. We give a positive answer to this question in the case when the line arrangement in $\mathbb{C}{P}^2$ is real, confirming that there exist exactly four such arrangements.

Minor changes and the misattributed names of complex reflection arrangements are corrected

References in corpus (1)

• Ramification conjecture and Hirzebruch's property of line arrangements

Cited by in corpus (1)

• Seshadri constants and special configurations of points in the projective plane