ABSTRACT
Let R Kx1 xn be a polynomial ring over a field K and let I be a monomial ideal of R generated by a finite set of monomials xv1 xvq. As usual we use xa as an abbreviation for xa11 xann , where a a1 an is in n . The three central objects of study here are the following blowup algebras: (a) the Rees algebra
RIt : R It Iiti Rt
where t is a new variable, (b) the associated graded ring
grIR : RI II2 IiIi1 RItR RI
with multiplication
a Ii1b I j1 ab Ii j1 a Ii b I j
and (c) the symbolic Rees algebra
RsI : R I1t I2t2 Iiti Rt
where Ii is the ith symbolic power of I.
