Multiple zeta values and periods of moduli spaces $\mathfrak{M}_{0,n}$
| dc.creator | Brown, Francis C. S. | |
| dc.date | 2006-06-17 | |
| dc.date.accessioned | 2026-07-07T07:17:24Z | |
| dc.date.available | 2026-07-07T07:17:24Z | |
| dc.description | In this paper we prove a conjecture due to Goncharov and Manin which states that the periods of the moduli spaces $\mathfrak{M}_{0,n}$ of Riemann spheres with $n$ marked points are multiple zeta values. In order to do this, we introduce a differential algebra of multiple polylogarithms on $\mathfrak{M}_{0,n}$, and prove that it is closed under the operation of taking primitives. The main idea is to apply a version of Stokes' formula iteratively, and to exploit the geometry of the moduli spaces to reduce each period integral to multiple zeta values. We also give a geometric interpretation of the double shuffle relations, by showing that they are two extremal cases of general product formulae for periods which arise by considering natural maps between moduli spaces. | |
| dc.description | 110 pages, 15 figures | |
| dc.identifier | https://arxiv.org/abs/math/0606419 | |
| dc.identifier | http://arxiv.org/abs/math/0606419 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/113925 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14G32; 11G55; 32G34 | |
| dc.title | Multiple zeta values and periods of moduli spaces $\mathfrak{M}_{0,n}$ | |
| dc.type | text |