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--- blog:2023-03-22 [2023/03/23 09:05] – [Skeleton] pzhou
+++ blog:2023-03-22 [2023/06/25 15:53] (current) – external edit 127.0.0.1
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+OK, I think this can be done in a local way.
+==== 2 dim ====
+Of course, the simplest way is to do a product. What's the local model? $\R^2$, $T^*\R^2$. What's the local model? Cylinder with two stops at one end. The neighborhood and thickening is nice.
+What happens, if you have 3 lines come together? Is there some parameter? I don't think so. Here is the reason. You can define skeleton basically by erecting a conormal, then put a lollipop at the end. There is no ambiguity at putting a lollipop. And if you have several such lollipop, these lollipops are disjoint.
+==== non-unimodular case? quotient? ====
+How to describe the upstair space $(t-1)^2 = uv$, and $(t-1) = (uv)^2$, and $t^2 - 1 = uv$? Maybe the first one is more serious. You can deform it, to $(t-1)(t-1-\epsilon)=uv$, or you can resolve it. I guess, we want to deform it.
+suppose we have several copies of this space, and we want to do multiplicative reduction, what do we do? We
+consider certain product, like $t_1 t_2 t_3^2 = b$ (say we want to do weighted proj space), and then we quotient out the fiber by something.
+Downstairs space, what do we do with the quotient step?