Moduli spaces ℳ2,1 and ℳ3,1

Abstract

The cell structure of the spaces ℳ2,1 and ℳ3,1 is considered. These are the spaces of complex curves of genus 2 and 3 with one marked point. For the space ℳ2,1, nine cells of the highest dimension 8 are described and their adjacency is studied. For the space ℳ3,1, a list of all 1726 cells of the highest dimension 14 (with orientation) is obtained. The list of adjacent couples of cells is also obtained. These lists can be found on the web.