In the previous chapters we focused on sets of reduced points X in (Formula Presented), that is, I(X)=I(X). We now relax this condition to study “sets of fat points”. Roughly speaking, given a set of reduced points X, we assign to each Pi∈ X a positive integer mi, called its multiplicity, and we consider the ideal I(Z)=⋂i=1sI(Pi)mi. We can then ask similar questions for the set of fat point Z defined by I(Z): when is Z arithmetically Cohen-Macaulay? If Z is ACM, what is its Hilbert function HZ? What is the bigraded minimal free resolution of I(Z)? We answer these questions in this chapter.
Fat points in (Formula Presented)
Guardo E.;Van Tuyl A.
2015-01-01
Abstract
In the previous chapters we focused on sets of reduced points X in (Formula Presented), that is, I(X)=I(X). We now relax this condition to study “sets of fat points”. Roughly speaking, given a set of reduced points X, we assign to each Pi∈ X a positive integer mi, called its multiplicity, and we consider the ideal I(Z)=⋂i=1sI(Pi)mi. We can then ask similar questions for the set of fat point Z defined by I(Z): when is Z arithmetically Cohen-Macaulay? If Z is ACM, what is its Hilbert function HZ? What is the bigraded minimal free resolution of I(Z)? We answer these questions in this chapter.File in questo prodotto:
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