Complex arrangements whose complement has Euler characteristic \(\pm 1\) (Q1382962)

This paper contains a proof of the following theorem: Let \(A\) be an arrangement of hyperplanes in \(\mathbb{C}^n\) such that the complement of the union of the hyperplanes has Euler characteristic \(\pm 1\). Then there exists an affine coordinate system such that the equations of the hyperplanes of \(A\) have rational coefficients. In fact it may be achieved that all of these coefficients are equal to \(0\) or \(1\). A simple example shows that this theorem does not hold for any Euler characteristic different from \(\pm 1\).