Rees algebra


In commutative algebra, the Rees algebra of an ideal I in a commutative ring R is defined to be
The extended Rees algebra of I is defined as
This construction has special interest in algebraic geometry since the projective scheme defined by the Rees algebra of an ideal in a ring is the blowing-up of the spectrum of the ring along the subscheme defined by the ideal.

Properties

The associated graded ring of I may be defined as
If R is a Noetherian local ring with maximal ideal, then the special fiber ring of I is given by
The Krull dimension of the special fiber ring is called the analytic spread of I.