Moduli Spaces and Multiple Polylogarithm Motives
نویسنده
چکیده
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 spacesM0,n of n-pointed stable curves of genus 0, and prove that the cohomology of the pair (M0,n−A,B−B∩A) is a framed mixed Tate motive whose period is that integral. It generalizes the results of A. Goncharov and Yu. Manin for multiple ζ-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.
منابع مشابه
Multiple Ζ–motives and Moduli Spaces M 0,n
Contents 1 Introduction and summary 2 Geometry of M 0,n+3 and divisors B 3 Forms Ω(ε) and divisors A(ε) 4 Multiple ζ–motives
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