Pretace
Introduction
Chapter 1.Hilbert scheme of points
1.1.General Results on the Hilbert scheme
1.2.Hilbert scheme of points on the plane
1.3.Hilbert scheme of points on a surface
1.4.Symplectic structure
1.5.The Douady space
Chapter 2.Framed moduli space of torsion free sheaves on p2
2.1.Monad
2.2.Rank 1 case
Chapter 3.Hyper-Kahler metric on(C2)[n]
3.1.Geometric invariant theory and the moment map
3.2.Hyper-Kghler quotients
Chapter 4.Resolution of simple singularities
4.1.General Statement
4.2.Dynkin diagrams
4.3.A geometric realization of the McKay correspondence
Chapter 5.Poinca％polynomials of the Hilbert schemes(1)
5.1.Perfectness of the Morse function arising from the moment map
5.2.Poincar~polynomial of f(C2)[n]
Chapter 6.Poinca％polynomials of Hilbert schemes(2)
6.1.Results on intersection cohomology
6.2.Proof of the formula
Chapter 7.Hilbert scheme on the cotangent bundle of a Riemann surface
7.1.Morse theory on holomorphic symplectic manifolds
7.2.Hilbert scheme of T*∑
7.3.Analogy with the moduli space of Higgs bundles
Chapter 8.Homology group of the Hilbert schemes and the Heisenberg algebra
8.1.Heisenberg algebra and Clifford algebra
8.2.CorresDondences
8.3.Main construction
8.4.Proof of Theorem 8.13
Chapter 9.Symmetric products of an embedded curve，symmetric flunctions
and vertex operators
9.1.Symmetric functions and symmetric groups
9.2. Grojnowski'S formulation
9.3.Symmetric products of an embedded CUrve
9.4.Vertex algebra
9.5. Moduli space of rank 1 sheaves
Bibliography
Index
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