---
date: 2022-12-26 18:36
modification date: Monday 26th December 2022 18:36:27
title: "Rees algebra"
aliases: [Rees algebra]
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Last modified date: NaN

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- Tags: 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- #todo/create-links 

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# Rees algebra

- $\Rees(I) \da \bigoplus_{n\geq 0} I^n \cong \bigoplus _{n\geq 0} I^n t^n \subseteq R[t]$ where $I^0 \da R$ and $\abs{t} = 1$.
- Generated by $I$ in degree 1.
- There is an embedding $R\to \Rees(I)_0$ where $r\mapsto r\cdot t^0$.
- If $I = \gens{g_1,\cdots, g_k}_R \subseteq R$ is fg, then $\Rees(I) \cong R[g_1 t,\cdots, g_k t]$.
- $\Rees(0) = R$ and $\Rees(R) = R[t]$.
- $\Rees(I) \cong \Rees(I^d)$ for any $d\geq 1$.