Rees algebra

Summary

The Rees algebra of an ideal $I$ of a commutative ring $R$ is the graded ring $R[It] = \bigoplus_{n \ge 0} I^n t^n$, a subring of the polynomial ring $R[t]$. It packs all the powers of $I$ into one ring, so that statements about all $I^n$ become statements about a single ring. Its quotient by $I R[It]$ is the associated graded ring, and in geometry it gives the blowing up along $I$.