UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

October 28, 2008

939 Evans Hall

3:45PM: Smoothable and Nonsmoothable Singularities

Robin Hartshorne

A 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 non-smoothable singularities, first considered by Pinkham.

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