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The easiest example I can think of is to consider the map $\mathbb{A}^1\to \mathbb{A}^1$ by sending $x\to x^2$, where $x$ is the coordinate. Then take the fibre over the origin, which would be $Spec k[x]/(x^2)$. The idea is that $x=0$ in the fibre should be counted "twice". There is lot more that one can say about why this is a useful, and perhaps someone else will. But let me just refer you to the book by Eisenbud and Harris for further discussion. |
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The easiest example I can think of is to consider the map $\mathbb{A}^1\to \mathbb{A}^1$ by sending $x\to x^2$, where $x$ is the coordinate. Then take the fibre over the origin, which would be $Spec k[x]/(x^2)$. The idea is that $x=0$ in the fibre should be counted "twice". |
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