Projective equivalence for the roots of unity

摘要

Let mu(infinity) subset of C be the collection of roots of unity and C-n := {(s(1), ..., s(n)) is an element of mu(n)(infinity): S-i not equal 0 S-j for any 1 <= i < j <= n}. Two elements (s(1), ..., s(n)) and (t(1), ..., t(n)) of C-n are said to be projectively equivalent if there exists gamma is an element of PGL(2, C) such that gamma(s(i)) = t(i) for any 1 <= i <= n. In this article, we will give a complete classification for the projectively equivalent pairs. As a consequence, we will show that the maximal length for the nontrivial projectively equivalent pairs is 14.