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Abstract: Given a graded algebra R over a field k, we look at the graded
Gorenstein Artin quotients A of R. In particular, when R is the
homogeneous coordinate ring of a zero-dimensional scheme in
projective space, we study under what conditions there are
Gorenstein Artin quotients of R with Hilbert function equal to the
Hilbert function of R in all degrees less than or equal to half
the socle degree. Similar results have been obtained by Iarrobino
and Kanev~\cite{Iarrobino-Kanev} and by Cho and
Iarrobino~\cite{Cho-Iarrobino} using inverse systems.
If \Delta is a Cohen-Macaulay simplicial complex and k[\Delta] the
corresponding Stanley-Reisner ring, we can take the quotient of
k[\Delta] by a regular sequence to get the coordinate ring of a
zero-dimensional scheme consisting of n distinct points in
projective space. We make some remarks on how this observation can
be used to give interesting examples of zero-dimensional schemes. In
particular, we get arithmetically Gorenstein subschemes if the
complex is Gorenstein, e.g. a simplicial polytope or a simplicial
sphere. We also get results about generalized stick figures
(cf. Geramita and Migliore~\cite{Geramita-Migliore}).
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