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- W2042843318 abstract "Earlier we showed that the Hilbert scheme of $n$ points in the plane can be identified with the Hilbert scheme of regular $S_n$ orbits on $C^{2n}$. Using this result, together with a recent theorem of Bridgeland, King and Reid on the generalized McKay correspondence, we prove vanishing theorems for tensor powers of tautological bundles on the Hilbert scheme. We apply the vanishing theorems to establish (among other things) the character formula for diagonal harmonics conjectured by Garsia and the author. In particular we prove that the dimension of the space of diagonal harmonics is equal to $(n+1)^{n-1}$." @default.
- W2042843318 created "2016-06-24" @default.
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- W2042843318 date "2002-08-01" @default.
- W2042843318 modified "2023-09-25" @default.
- W2042843318 title "Vanishing theorems and character formulas for the Hilbert scheme of points in the plane" @default.
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- W2042843318 doi "https://doi.org/10.1007/s002220200219" @default.
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