Periods on the moduli space of genus 0 curves

TL;DR

This paper presents a combinatorial method for computing bases of cohomology spaces related to multizeta values on genus 0 moduli spaces, enhancing understanding of their algebraic structure.

Contribution

It introduces a new combinatorial recipe for constructing bases of specific cohomology spaces associated with genus 0 moduli spaces.

Findings

Provides explicit bases for cohomology spaces linked to multizeta values

Develops a combinatorial approach using oriented polygons

Advances computational techniques for moduli space cohomology

Abstract

This report outlines a combinatorial recipe for computing the bases, whose elements are oriented polygons, of two cohomology spaces associated to multizeta values: the top dimensional de Rham cohomology of moduli spaces of genus 0 complex pointed curves and the top dimensional de Rham cohomology of certain partial compactifications of these moduli spaces.