Archiv der Mathematik

, Volume 75, Issue 1, pp 59-64

First online:

Hilbert schemes of a surface and Euler characteristics

  • M. A. A. de CataldoAffiliated withDepartment of Mathematics, SUNY at Stony Brook, Stony Brook, NY 11794-3651, USA

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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.