Calculating Archimedean Height Pairing via generalized cross-ratio

Abstract

During the last several years, Spencer Bloch emphasized that Archimedean hight pairings between two homologically trivial cycles of complimentary arithmetic dimensions, or the closely related classes in the biextension, should lead to interesting analogs of the classical cross ratio. In this note I calculate such a generalized cross-ratio for planes in the projective space.