The moduli space of curves is rigid
arXiv:math/0509567
Abstract
We prove that the moduli stack of stable curves of genus g with n marked points is rigid, i.e., has no infinitesimal deformations. This confirms the first case of a principle proposed by Kapranov. It can also be viewed as a version of Mostow rigidity for the mapping class group.
11 pages. v2: Proof rewritten to avoid use of log structures. Example of nonrigid moduli space of surfaces added