4
votes
1answer
173 views

Kodaira classification and the McKay correspondence

Kodaira's table of singular fibers has a singular fiber for each of $\tilde{A}_n$, $\tilde{D}_n$, $\tilde{E}_6$, $\tilde{E}_7$, and $\tilde{E}_8$; these are chains or cycles of (-2)-curves connected ...
3
votes
0answers
285 views

Blowing up a projective surface

Let $X$ be a smooth degree $d$ ($d>5$) surface in $\mathbb{P}^3$. We now blow up $X$ at a point, embed it in some projective space, and and consider a projection of it into $\mathbb{P}^3$. The ...
9
votes
1answer
945 views

Du Val singularity of type G=A,D,E and “small” representations of G

We all know that a simple singularity $W_G(x_1,x_2,x_3)=0$ of type G=A,D,E has the following nice deformation involving the Cartan subalgebra $\mathfrak{h}$ of the Lie algebra $\mathfrak{g}$ of $G$. ...