User yougeeaw - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T20:58:11Z http://mathoverflow.net/feeds/user/14559 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/24132/what-are-examples-of-mathematical-concepts-named-after-the-wrong-people-stigler/69830#69830 Answer by Yougeeaw for What are examples of mathematical concepts named after the wrong people? (Stigler's law) Yougeeaw 2011-07-08T21:08:57Z 2011-07-08T21:08:57Z <p>The notion of Frobenius manifold is due to Dubrovin</p> http://mathoverflow.net/questions/62544/homotopy-type-of-hilbert-schemes-of-points-of-mathbb-c2 Homotopy type of Hilbert schemes of points of \$\mathbb C^2\$ Yougeeaw 2011-04-21T15:55:06Z 2011-04-22T16:24:52Z <p>Let \$X=\mathbb C^2\$, let \$X^{[n]}\$ be the Hilbert scheme of length \$n\$ 0-cycles in \$X\$, and let \$X^{[n]}_0\$ be the closed subscheme formed by the 0-cycles supported at 0. As far as I know \$X^{[n]}_0\$ and \$X^{[n]}\$ have the same homotopy type. Can anybody suggest a proof? (according to Nakajima this can be proved by adapting an argument of Slodowy (Four lectures on simple groups and singularities, Section 4.3) but I am unable to do it...)</p> http://mathoverflow.net/questions/62544/homotopy-type-of-hilbert-schemes-of-points-of-mathbb-c2/62634#62634 Comment by Yougeeaw Yougeeaw 2011-09-01T18:10:10Z 2011-09-01T18:10:10Z The idea is intuitively attractive, but I am unable to make it into a rigorous proof. http://mathoverflow.net/questions/62544/homotopy-type-of-hilbert-schemes-of-points-of-mathbb-c2/62578#62578 Comment by Yougeeaw Yougeeaw 2011-09-01T18:09:24Z 2011-09-01T18:09:24Z Yep, you get to proving the isomorphism of the homotopy groups by using relative Hurewicz. And then you prove that the two spaces are homotopy equivalent. http://mathoverflow.net/questions/24132/what-are-examples-of-mathematical-concepts-named-after-the-wrong-people-stigler/69830#69830 Comment by Yougeeaw Yougeeaw 2011-08-31T10:17:11Z 2011-08-31T10:17:11Z Why -2 votes??? http://mathoverflow.net/questions/62544/homotopy-type-of-hilbert-schemes-of-points-of-mathbb-c2/62578#62578 Comment by Yougeeaw Yougeeaw 2011-04-22T12:06:16Z 2011-04-22T12:06:16Z Thank you. I can follow this until proving the isomorphism between the homologies. I have some problems with the homotopy. But I will review the argument again.