JournalsjemsVol. 10 , No. 1DOI 10.4171/jems/109

A remark on the homotopical dimension of some moduli spaces of stable Riemann surfaces

  • Gabriele Mondello

    Università di Roma 'La Sapienza', Italy
A remark on the homotopical dimension of some moduli spaces of stable Riemann surfaces cover

Abstract

Using a result of Harer, we prove certain upper bounds for the homotopical/cohomological dimension of the moduli spaces of Riemann surfaces of compact type, of Riemann surfaces with rational tails and of Riemann surfaces with at most kk rational components. These bounds would follow from conjectures of Looijenga and Roth-Vakil.