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We study the natural Gieseker and Uhlenbeck compactifications of the rational Calogero-Moser phase space. The Gieseker compactification is smooth and provides a small resolution of the Uhlenbeck compactification. We use the resolution to compute the stalks of the IC-sheaf of the Uhlenbeck compactification. I'd say that if one can compute the Poincaré polynomialfor intersection cohomology without a computer then, probably, there is a small resolution which gives it.(J. Bernstein)

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