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Tables of Contents for Lectures on Hilbert Schemes of Points on Surfaces
Chapter/Section Title
Page #
Page Count
Preface
ix
Introduction
1
4
Hilbert scheme of points
5
12
General Results on the Hilbert scheme
5
2
Hilbert scheme of points on the plane
7
5
Hilbert scheme of points on a surface
12
1
Symplectic structure
13
2
The Douady space
15
2
Framed moduli space of torsion free sheaves on P2
17
12
Monad
18
6
Rank 1 case
24
5
Hyper-Kahler metric on (C2)[n]
29
18
Geometric invariant theory and the moment map
29
8
Hyper-Kahler quotients
37
10
Resolution of simple singularities
47
12
General Statement
47
2
Dynkin diagrams
49
3
A geometric realization of the McKay correspondence
52
7
Poincare polynomials of the Hilbert schemes (1)
59
14
Perfectness of the Morse function arising from the moment map
59
4
Poincare polynomial of (C2)[n]
63
10
Poincare polynomials of Hilbert schemes (2)
73
6
Results on intersection cohomology
73
2
Proof of the formula
75
4
Hilbert scheme on the cotangent bundle of a Riemann surface
79
10
Morse theory on holomorphic symplectic manifolds
79
1
Hilbert scheme of T*Σ
80
5
Analogy with the moduli space of Higgs bundles
85
4
Homology group of the Hilbert schemes and the Heisenberg algebra
89
16
Heisenberg algebra and Clifford algebra
89
2
Correspondences
91
2
Main construction
93
3
Proof of Theorem 8.13
96
9
Symmetric products of an embedded curve, symmetric functions and vertex operators
105
20
Symmetric functions and symmetric groups
105
4
Grojnowski's formulation
109
1
Symmetric products of an embedded curve
110
4
Vertex algebra
114
7
Moduli space of rank 1 sheaves
121
4
Bibliography
125
6
Index
131