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Abstract:
Recently, there has been some progress in the area of
codimension three level algebras: graded Artinian algebras with socle
in the same degree. In the special case of Gorenstein algebras of
codimension three there are lots of nice properties due to the very
explicit structure theorem of Buchsbaum and Eisenbud. For example,
there are nice irreducible and smooth parameter spaces and the possible
Hilbert functions and Betti numbers are well understood. However,
it turns out that these properties fail to hold as soon as the
Cohen-Macaulay type is greater than one. This will be a report on
joint work with Anthony Iarrobino on reducible parameter spaces and
with Fabrizio Zanello on non-unimodality and lack of the weak
Lefschetz property.
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