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--- blog:2023-08-05 [2023/08/05 22:12] – pzhou
+++ blog:2023-08-05 [2023/08/06 04:10] (current) – pzhou
@@ Line 2: / Line 2: @@
   * write up the notes that are useful for myself.
   * why quiver gauge theory has anything to do with Kac-Moody algebra?
+The stuff that I typed up below, are so incoherent and dreamy, that I don't know what am I talking about.
+So they should be either cleaned up or deleted.
+I also cleaned up some to read papers.
+I don't think I want to write up the example computation of the spaces.
 ===== Statements,  Examples about Coulomb branches =====
@@ Line 37: / Line 44: @@
 In the example of $\P^1$, at point $[1;0]$, where we use $T_2 / T_1$ as local coordinates. Let me say, the normal bundle is cashed in for $Y_2 - Y_1$. Then, we say
 $$ [\P^1] = \frac{[0]}{Y_2 - Y_1} + \frac{[\infty]}{Y_1 - Y_2}. $$
-The homology classes are in $H_2^T(\P^1) = H^0$.
+If we understand both sides as cohomology, then both are in degree $0$, $deg([0])=2$ but $deg(Y_i)=2$, so they cancel.
+Why does localization to fixed point works? Why does it play well with convolution? Isn't convolution very complicated?