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--- blog:2023-02-25 [2023/02/26 16:17] – pzhou
+++ blog:2023-02-25 [2023/06/25 15:53] (current) – external edit 127.0.0.1
@@ Line 38: / Line 38: @@
 We may define the subcategory to be kill as, things killed by all the positive degree morphism in  $End(S)_{>0} = \oplus_{n>0} Hom(O, S^n)$.
-Finally, let's say what this means on the equivariant A-side. $S$ is the shift to the right.
+Finally, let's say what this means on the equivariant A-side. $S$ is the shift of the equivariant positiion to the right. so indeed, on the constructible sheaf side, it worked. Now, how to get a morphism? Well, there is only one morphism in the base, between two lines, and there might be more in the fiber.
+In general, for more general GIT quotient by $(\C^*)^n$, what's the story?
+===== Universal Window? ======
+OK, let's consider this. On the B-side, we have $\C^N$. The structure sheaf is mirror to the totally positive real line.(when we do the actual mapping, need to backward wrap a tiny little bit.)
+What's its shadow on the base $((\C^*)^k)^\vee$? Well, it is the positive real line. Is it really away from the discrimiant locus?
+Consider hte equation for $1+x+y+t xy = 0$, where $t$ is the parameter, when is the equation singular? it is at $t=1$. darn it. why it has to pass through the critical point?
+Consider the case of $(1,1,-2)$, window size is 2.
+===== B-side Unstable Loci =====
+OK, what we do? In the toric case, we pick a  character on the B-side GIT quotient, hence a 1PS on the A-side base, in particular, a loop, an element in HH. or projective HH. We do the shift, look for the morphism in the wrapped category
+===== Non CY case? =====