ar X iv : m at h / 01 11 04 7 v 2 [ m at h . A G ] 2 6 Fe b 20 02 HILBERT SCHEMES AND W ALGEBRAS
نویسندگان
چکیده
We construct geometrically the generating fields of a W algebra which acts irreducibly on the direct sum of the cohomology rings of the Hilbert schemes X [n] of n points on a projective surface X for all n ≥ 0. We compute explicitly the commutators among the Fourier components of the generating fields of the W algebra, and identify this algebra with a W1+∞-type algebra. A precise formula of certain Chern character operators, which is essential for the construction of the W algebra, is established in terms of the Heisenberg algebra generators. In addition, these Chern character operators are proved to be the zero-modes of vertex operators.
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We construct geometrically a W algebra which acts irreducibly on the direct sum of the cohomology rings of the Hilbert schemes X [n] of n points on a projective surface X for all n ≥ 0. We compute explicitly the commutators among a set of linear basis elements of the W algebra, and identify this algebra with a W1+∞-type algebra. A precise formula of certain Chern character operators, which is e...
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