Hilbert schemes of a surface and Euler characteristics
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- de Cataldo, M. Arch. Math. (2000) 75: 59. doi:10.1007/s000130050474
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We use basic algebraic topology and Ellingsrud-Stromme results on the Betti numbers of punctual Hilbert schemes of surfaces to compute a generating function for the Euler characteristic numbers of the Douady spaces of “n-points” associated with a complex surface. The projective case was first proved by L. Göttsche.