Index
(C
2
)[n],
8, 24, 36, 41, 47, 59, 63, 81
e 106 Ln,
n
H∗(X[n])
is a graded Hopf algebra, 110
is a represetnation of the Heisenberg su-
peralgebra, 94
HilbX , 5
hn, 106

Σ, 85, 111
Λ, 106
M(r, n), 17, 45
M0(r, n), 43, 45
Mreg(r,
0
n), 43, 45
, 106
P [i], 93
Pα[i], 94
Sn(C 2
), 26, 34, 41

nX,
75

nX,
7
SnX,
6
X[n],
6
ADHM datum, 43
affine algebro-geometric quotient, 29
ALE space, 18, 46, 47, 52, 83, 124
anti-self-dual connection, 42, 43
Beilinson spectral sequence, 18
Borel-Moore homology, 91
Calogero-Moser system, 42
Chern class, 107
Clifford algebra, 89
complete symmetric function, see hn
conformal vector, 115
conjugacy classes of symmetric groups, 108
coproduct, 109
correspondence, 92
cotangent bundle of a Riemann surface, 80
crepant resolution, 56
C

-action, 79, 80
decomposable diagonal class, 26, 53
decomposition theorem, 74
Douady space, 15
Douady-Barelet morphism, 15
Dynkin diagram, 49
elementary symmetric function, see en
equivariant K-group, 110
equivariant cohomology, 62
Fock space, 89
framed moduli space
of anti-self-dual connections, see M0
reg
(r, n)
of ideal instantons, see M0(r, n)
of torsion free sheaves, see M(r, n)
G¨ottsche’s formula, 69, 73, 84, 90, 94
geometric invariant theory quotient, 35
graded Hopf algebra, 109
Grojnowski’s formulation, 109
Grothendieck group
of algebraic vector bundles, 54
of coherent sheaves, 54, 103
of complexes of algebraic vector bundles,
54
of equivariant topological vector bundles,
110
Heisenberg algebra, 89
Heisenberg superalgebra, 90
Hilbert scheme
functor, see HilbX
Grothendieck’s theorem, 5
of points
definition, 6
on the cotangent bundle, 80
on the plane, see (C
2
)[n]
Hilbert-Chow morphism, 7, 10, 75
Hodge numbers of
X[n],
77, 95
holomorphic symplectic form, 10, 13, 79, 85
hyper-K¨ahler
manifold, 38
moment map, 38
quotient, 37, 39
structure, 11, 14, 37, 47
ideal instanton, 45
instanton, 42, 46
integrable system, 42, 86
intersection cohomology, 73
intersection pairing, 92
Lagrangian, 79
131
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