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)

#### 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.
##### Scheda breve Scheda completa Scheda completa (DC)
2015
978-3-319-24164-7
978-3-319-24166-1
Arithmetically Cohen-Macaulay (ACM)
Castelnuovo Mumford Regularity
Hilbert Function
Horizontal Rule
Minimal Free Resolution
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/20.500.11769/505978`
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