Moduli Spaces and Multiple Polylogarithm Motives

Details Moduli Spaces and Multiple Polylogarithm Motives Moduli Spaces and Multiple Polylogarithm Motives

2006-10-23

arxiv.org/abs/math/0610670v1

Mathematics

Algebraic Geometry

24 pages, 2 figures, to appear in Adv.in Math

Scientific paper

In this paper, we give a natural construction of mixed Tate motives whose periods are a class of iterated integrals which include the multiple polylogarithm functions. Given such an iterated integral, we construct two divisors $A$ and $B$ in the moduli spaces $\mathcal{\bar{M}}_{0,n}$ of $n$-pointed stable curves of genus 0, and prove that the cohomology of the pair $(\mathcal{\bar{M}}_{0,n}-A,B-B\cap A)$ is a framed mixed Tate motive whose period is that integral. It generalizes the results of A. Goncharov and Yu. Manin for multiple zeta values. Then we apply our construction to the dilogarithm and calculate the period matrix which turns out to be same with the canonical one of Deligne.

Affiliated with

Also associated with

No associations

Rating

Moduli Spaces and Multiple Polylogarithm Motives does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Moduli Spaces and Multiple Polylogarithm Motives, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Moduli Spaces and Multiple Polylogarithm Motives will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-277234