Deformation Theory
Seiten
2012
Springer-Verlag New York Inc.
978-1-4614-2520-5 (ISBN)
Springer-Verlag New York Inc.
978-1-4614-2520-5 (ISBN)
This first textbook on deformation theory begins by studying what happens over small infinitesimal deformations, and then gradually builds up to more global situations. The author provides plenty of motivation, including numerous exercises and examples.
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.
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.
First-Order Deformations.- Higher-Order Deformations.- Formal Moduli.- Global Questions.
| Reihe/Serie | Graduate Texts in Mathematics ; 257 |
|---|---|
| Zusatzinfo | 19 Illustrations, black and white; VIII, 234 p. 19 illus. |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| Schlagworte | Deformationen (Mathematik) • deformation theory • first-order deformations • formal moduli • higher-order deformations • Hilbert scheme • infinitesimal lifting property • invertible sheaves • Vector Bundles |
| ISBN-10 | 1-4614-2520-4 / 1461425204 |
| ISBN-13 | 978-1-4614-2520-5 / 9781461425205 |
| Zustand | Neuware |
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