Is the Springer resolution a blow-up? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T19:30:31Z http://mathoverflow.net/feeds/question/102013 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/102013/is-the-springer-resolution-a-blow-up Is the Springer resolution a blow-up? Zhaoting Wei 2012-07-12T04:13:48Z 2012-07-12T08:43:10Z <p>Let's consider the Springer resolution of the nilpotent cone $\mathcal{N}$ of a complex semisimple Lie algebra $\mathfrak{g}$, which is $$\widetilde{\mathcal{N}}=T^*\mathcal{B}\rightarrow \mathcal{N}.$$ It is a resolution of singularity of $\mathcal{N}$. ( For the construction of Springer resolution you can see section 6 of "Geometric Methods in Representation Theory of Hecke Algebras and Quantum Groups" .)</p> <p>My question is: is it a blow-up along some subscheme of $\mathcal{N}$?</p> <p>Or for the simplest case, where $\mathfrak{g}=sl(2,\mathbb{C})$. Now $$\mathcal{N}= {x^2=yz} \in \mathbb{C}^3$$ In this case is $\widetilde{\mathcal{N}}$ the same as the blow-up at $0$?</p>