In the fall semester of 1979 I gave a course on deformation theory at Berkeley. My goal was to understand completely Grothendieck’s local study of the Hilbert scheme using the cohomology of the normal bundle to characterize the Zariski tangent space and the obstructions to deformations. At the same time I started writing lecture notes for the course.However,the writing project soon foundered as the subject became more intricate, and the result was no more than of a projected thirteen sections, corresponding roughly to s- tions 1, 2, 3, 5, 6 of the present book. These handwritten notes circulated quietly for many years until David Eisenbud urged me to complete them and at the same time (without consuing me) mentioned to an editor at Springer, “You know Robin has these notes on deformation theory, which could easily become a book.
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