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

Lν

Σ, 85, 111

Λ, 106

M(r, n), 17, 45

M0(r, n), 43, 45

Mreg(r,

0

n), 43, 45

mν , 106

P [i], 93

Pα[i], 94

Sn(C 2

), 26, 34, 41

Sν

nX,

75

Sν

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

(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

Lν

Σ, 85, 111

Λ, 106

M(r, n), 17, 45

M0(r, n), 43, 45

Mreg(r,

0

n), 43, 45

mν , 106

P [i], 93

Pα[i], 94

Sn(C 2

), 26, 34, 41

Sν

nX,

75

Sν

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