Mathematics

M. Kapranov proposed the following conjecture about the deformations of a smooth scheme:
Let X be a smooth scheme, and let X_1 be the moduli space of deformations of X, X_2 the moduli space of deformations of X_1, and so on. Then X_dim(X) is rigid, that is it does not have infinitesimal deformations. In this seminar we will prove this conjecture for the moduli space \bar M_0,n, parametrizing pointed rational curves, over a field K of positive characteristic. As a consequence, Working over the ring of Witt vectors W(K), we will derive that, over K, the automorphism group of \bar M_0,n is S_n for n>=5.