In Deligne-Mumford's "The irreducibility of the space of curves of given genus", the authors use the "Schlessinger's theory", and refer his "thesis". Where can I read it? It seems to be different from his paper "Functors of Artins rings".

This theory of deformation (of singular schemes) are used in many papers, for example Deligne-Rapoport's "Les schemas de modules de courbes elliptiques". (And the theory of deformation of "curves + a section", used in Deligne-Rapoport, seems not to be written in his thesis. Please suggest me some references of it.)