Rees algebra

In commutative algebra, the Rees algebra of an ideal "I" in a commutative ring "R" is defined to be formula_1The extended Rees algebra of "I" (which some authors refer to as the Rees algebra of "I") is defined asformula_2This 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.
Relationship with other blow-up algebras.
The associated graded ring of "I" may be defined asformula_9If "R" is a Noetherian local ring with maximal ideal formula_10, then the special fiber ring of "I" is given byformula_11The Krull dimension of the special fiber ring is called the analytic spread of "I".