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--- blog:2023-07-30 [2023/07/31 07:08] – pzhou
+++ blog:2023-07-30 [2023/07/31 08:24] (current) – [Coulomb branches] pzhou
@@ Line 18: / Line 18: @@
 OK, now we need to abelianize, so we introduce
 $$ \frac{x_{2,i}^+ - x_{2,j}^+}{y_{2,i}-y_{2,j}}. $$
+Well, here is the trouble, remember the case for $T^*\P^2$? Or the simpler one $(1)-(1)$? If you go by the rule of $x_1^+x_1^- = y_1-y_2, \quad x_2^+x_2^-=y_1-y_2$, then you lose. You know what this is suppose to be. You need more generators and relations. You need the $r_{1,1}$ and $r_{-1,-1}$. Then you are in good shape. In general, you need to take a good size of blobs of weights, and do those generators, and get those relations.
+Then, when you do the blow-up, you can do the simple things. Just pick some variables and blow them up.
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