Geometry of the 1-skeleta of singular nerves of moduli spaces of Riemann surfaces

Cornalba (Ann Mat Pura Appl 149:135–151, 1987 ) classified the components of the singular locus of the moduli space of compact Riemann surfaces of genus g ≥ 2 . Here we consider the problem of describing the intersections of these components by examining certain nerves of the cover of singular locus that the Cornalba components provide. We give a description of the 1-skeleton of such nerves which significantly extends the results of our earlier paper written together with A. Weaver where we considered a coarser cover of the singular locus. We compare the results of our earlier work with those of the present one in terms of certain natural simplicial covering maps between them.