Real Grassmann Polylogarithms and Chern Classes

Details Real Grassmann Polylogarithms and Chern Classes Real Grassmann Polylogarithms and Chern Classes

1994-07-18

arxiv.org/abs/alg-geom/9407010v1

Mathematics

Algebraic Geometry

42 pages, amslatex

Scientific paper

In this paper we define real grassmann polylogarithms, which are real single valued analogues of the grassmann polylogarithms (or higher logarithms) defined by Hain and MacPherson. We prove the existence of all such real grassmann polylogs, at least generically. We also prove that the canonical choice of such an m-polylogarithm represents the Beilinson Chern class on the rank m part of the algebraic K-theory of the generic point of every complex algebraic variety. One part of each such grassmann m-polylogarithm is a real, single-valued function defined generically on the grassmannian of m planes in C^{2m}. We prove that this function represents the Borel regulator (up to a factor of 2) on K_{2m-1} of all number fields.

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