Holomorphic differential forms on moduli spaces of stable curves

Abstract

We prove that the space of holomorphic p-forms on the moduli space overline{mathcal {M}}_{g,n} of stable curves of genus g with n marked points vanishes for p=14, 16, 18 unconditionally and also for p=20 under a natural assumption in the case g=3. This result is consistent with the Langlands program and it is obtained by applying the Arbarello–Cornalba inductive approach to the cohomology of moduli spaces.