Components of the Space Parametrizing Graded Gorenstein Artin Algebras with a given Hilbert Function
نویسندگان
چکیده
We give geometric constructions of families of graded Gorenstein Artin algebras, some of which span a component of the space Gor(T ) parametrizing Gorenstein Artin algebras with a given Hilbert function T . This gives a lot of examples where 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.
منابع مشابه
Gorenstein algebras of embedding dimension four : Components of P Gor ( H ) for H = ( 1 , 4 , 7 , . . . , 1 )
A Gorenstein sequence H is a sequence of nonnegative integers H = (1, h1, . . . , hj = 1) symmetric about j/2 that occurs as the Hilbert function in degrees less or equal j of a standard graded Artinian Gorenstein algebra A = R/I , where R is a polynomial ring in r variables and I is a graded ideal. The scheme PGor(H) parametrizes all such Gorenstein algebra quotients of R having Hilbert functi...
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