Components of the space parametrizing graded Gorenstein Artin algebras with a given Hilbert function. (English) Zbl 0940.13009
Author’s abstract: We give geometric constructions of families of graded Gorenstein Artin algebras, some of which span a component of the space \(\text{Gor}(T)\) parametrizing Gorenstein Artin algebras with a given Hilbert function \(T\). This gives a lot of examples where \(\text{Gor}(T)\) is reducible. We also show that the Hilbert function of a codimension four Gorenstein Artin algebra can have an arbitrarily long constant part without having the weak Lefschetz property.
Reviewer: R.Fröberg (Stockholm)
MSC:
13C14 | Cohen-Macaulay modules |
13E10 | Commutative Artinian rings and modules, finite-dimensional algebras |
13D40 | Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series |
14M05 | Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) |