The Mixed Hodge structure on the fundamental group of a complement of hyperplanes
by
Yukihito Kawahara
Tokyo metropolitan university

The complement of an arrangement of hyperplanes is a good example of the mixed Hodge structure on the fundamental group of an algebraic variety. We compute its isomorphic class using iterated integrals and then get the cross ratio of a arrangement that is the combinatorial and projective invariant. So cross ratio equivalent arrangements are isomorphic. Moreover a isomorphism of polarized mixed Hodge structures on the fundamental group induce cross ratio equivalent arrangements.

Date received: June 3, 1999