The moduli space of curves is rigid

Research paper by Paul Hacking

Indexed on: 28 Aug '08Published on: 28 Aug '08Published in: Mathematics - Algebraic Geometry


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.