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Abstract: Let I be the defining ideal of a set of points in P^2. Generally, not
too much is known about the Rees algebra of I, but certain pieces of it are
always describable and appear to be "nice". In this talk, I will look at the
pieces of the Rees algebra of I, which are the Rees algebras of the ideals
generated by homogeneous pieces of I, and discuss their asymptotic behaviour.
More precisely, I will show that when the degree of the homogeneous pieces of I
are big enough, these Rees algebras are always Cohen-Macaulay, and if we take
the degrees to be even bigger, these Rees algebra stay Cohen-Macaulay and are
generated by quadratics. I will also make some conjecture about the resolution
of these Rees algebras. The same argument can be extended to a class of certain
codimension two perfect ideals.
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