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Cấu trúc
1441915958
Deformation Theory
Preface
Contents
Introduction
1 First-Order Deformations
1. The Hilbert Scheme
2. Structures over the Dual Numbers
3. The Ti Functors
4. The Infinitesimal Lifting Property
5. Deformations of Rings
2 Higher-Order Deformations
6. Subschemes and Invertible Sheaves
7. Vector Bundles and Coherent Sheaves
8. Cohen--Macaulay in Codimension Two
9. Complete Intersections and Gorenstein in Codimension Three
10. Obstructions to Deformations of Schemes
11. Obstruction Theory for a Local Ring
12. Dimensions of Families of Space Curves
13. A Nonreduced Component of the Hilbert Scheme
3 Formal Moduli
14. Plane Curve Singularities
15. Functors of Artin Rings
16. Schlessinger's Criterion
17. Hilb and Pic are Pro-representable
18. Miniversal and Universal Deformations of Schemes
19. Versal Families of Sheaves
20. Comparison of Embedded and Abstract Deformations
21. Algebraization of Formal Moduli
22. Lifting from Characteristic p to Characteristic 0
4 Global Questions
23. Introduction to Moduli Questions
24. Some Representable Functors
25. Curves of Genus Zero
26. Moduli of Elliptic Curves
27. Moduli of Curves
28. Moduli of Vector Bundles
29. Smoothing Singularities
References
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