Hello Everyone,

I am thinking on calculating the motive of Hilbert scheme of points on a smooth variety, of any dimension. There is a famous paper by Gottsche that calculates the Hilbert scheme of points on a smooth surface, which uses a cell decomposition of punctual Hilbert scheme of points on the plane. I am wondering if a similar results hold for punctual Hilbert scheme of any dimension, or at least is it known that such cell decomposition exists?

I apologize if this is a stupid question.

Best, minimax