Index (C 2 ) [n] , 8, 24, 36, 41, 47, 59, 63, 81 en, 106 L n H∗(X[n]) is a graded Hopf algebra, 110 is a represetnation of the Heisenberg su- peralgebra, 94 Hilb X , 5 hn, 106 LνΣ, 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 P α [i], 94 Sn(C 2 ), 26, 34, 41 SnX, ν 75 SnX, ν 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 M reg 0 (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 Hilb X 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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