most recent 30 from http://mathoverflow.net 2013-05-21T01:42:12Z http://mathoverflow.net/feeds/question/121941 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/121941/rationality-for-generating-series-for-hilbert-scheme-of-points-of-curves-with-tor xf495 2013-02-15T20:33:23Z 2013-02-15T20:33:23Z

<p>More concretely, let $I$ be a monimial ideal in $\mathbb{C}[x_1,\ldots,x_n]$ such that the ring $A=\mathbb{C}[x_1,\ldots,x_n]/I$ is one dimensional. Let $X=\operatorname{Spec}A$, and let $X^{[n]}$ be the punctual Hilbert scheme of points located at the origin. Then is it true that the generating series for Euler characteristic $\sum_{n}\chi(X^{[n]})t^n$ is rational?</p>