Hilbert scheme punctual

In section 2.2 we consider the punctual Hilbert schemes Hilbn(fc[[x, y]]). We give a cell decomposition of the strata and so determine their Betti numbers. I have published most of the results of this section in a different form in [Gottsche (3)]. They have afterwards been used in [Iarrobino-Yameogo (1)] to study the structure of the cohomology ring of the Gt- We also recall the results of [Ellingsrud-Str0mme (1),(2)] on a cell decomposition of Hilb"(fc[[x,j/]]) and P. ... 

Another proof of the irreducibility of the punctual Hilbert scheme of a smooth surface, preprint 1992. 

Algebraic families on an algebraic surface II, the Picard scheme of the punctual Hilbert scheme, Amercan Journal of Math. 95 (1973), 660-687. 

Betti numbers for the Hilbert function strata of the punctual Hilbert scheme in two variables, Manuscripta Math. 66 (1990), 253-259. 

Punctual Hilbert schemes, Bull. Amer. Math. Soc. 78 (1972), 819-823. 

In chapter 1 we recall some fundamental facts, that will be used in the rest of the book. First in section 1.1, we give the definition and the most important properties of Xfnl then in section 1.2 we explain the Weil conjectures in the form in which we are later going to use them in order to compute Betti numbers of Hilbert schemes, and finally in section 1.3 we introduce the punctual Hilbert scheme, which parametrizes subschemes concentrated in a point of a smooth variety. We hope that the non-expert reader will find in particular sections 1.1 and 1.2 useful as a quick reference. 

An intersection number for the punctual Hilbert scheme of a surface, preprint, alg-... 

C17] [fog 2] J. FOGARTHY.- The Picard scheme of the punctual Hilbert Scheme. American Journal of Mathematics (1973). 

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