On the Betti numbers of some Gorenstein ideals

Details On the Betti numbers of some Gorenstein ideals On the Betti numbers of some Gorenstein ideals

1994-06-20

arxiv.org/abs/math/9406208v1

Mathematics

Commutative Algebra

Scientific paper

Assume $R$ is a polynomial ring over a field and $I$ is a homogeneous Gorenstein ideal of codimension $g\ge3$ and initial degree $p\ge2$. We prove that the number of minimal generators $\nu(I_p)$ of $I$ that are in degree $p$ is bounded above by $\nu_0={p+g-1\choose g-1}-{p+g-3\choose g-1}$, which is the number of minimal generators of the defining ideal of the extremal Gorenstein algebra of codimension $g$ and initial degree $p$. Further, $I$ is itself extremal if $\nu(I_p)=\nu_0$.

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