Artinian Gorenstein algebras of embedding dimension four: Components of PGor(H) for H=(1,4,7,..., 1)

Details Artinian Gorenstein algebras of embedding dimension four: Components of PGor(H) for H=(1,4,7,..., 1) Artinian Gorenstein algebras of embedding dimension four: Components of PGor(H) for H=(1,4,7,..., 1)

2004-12-23

arxiv.org/abs/math/0412466v1

Mathematics

Commutative Algebra

29 pages. To appear Vasconcelos special issue of JPAA

Scientific paper

We first determine all height four Gorenstein sequences beginning H=(1,4,7,...), and we show that their first differences satisfy $\Delta H_{\le j/2}$ is an O-sequence. We then study the family PGor(H) parametrizing all graded Artinian Gorenstein [AG] quotients A=R/I of the polynomial ring R=K[w,x,y,z] having a Hilbert function H as above. We give a structure theorem for such AG quotients with $I_2\cong < wx,wy,wz>$. For most H this subfamily forms an irreducible component of PGor(H), and for a slightly more restrictive set, PGor(H) has several irreducible components. M. Boij and others had already shown that PGor(T) is reducible for certain Gorenstein sequences T in codimensions at least four.

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