3:45PM: Smoothable and Nonsmoothable SingularitiesRobin HartshorneA variety X_0 over an algebraically closed field k is *smoothable* if there exists a flat family X/T with T finite type integral curve over k, and a point 0 in T such that the fiber over 0 is X_0 and the fibers X_t are smooth for t different from 0. We give an infinitesimal condition for X_0 to be smoothable, which allows us to give some interesting examples of nonsmoothable singularities, first considered by Pinkham.
