Deformation Theory

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 [...]
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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 timeIstartedwritinglecturenotesforthecourse.However, thewritingproject soon foundered as the subject became more intricate, and the result was no more than ?ve 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 consu- ing me) mentioned to an editor at Springer, You know Robin has these notes on deformation theory, which could easily become a book. When asked by Springer if I would write such a book, I immediately refused, since I was then planning another book on space curves. But on second thought, I decided this was, afterall, aworthyproject, andthatbywritingImight?nallyunderstand the subject myself. So during 2004 I expanded the old notes into a rough draft, which I used to teach a course during the spring semester of 2005. Those notes, rewritten once more, with the addition of exercises, form the book you are now reading. Mygoalinthisbookistointroducethemainideasofdeformationtheoryin algebraicgeometryandtoillustratetheiruseinanumberoftypicalsituations."