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Keywords:
associated graded ring; fibre product; connected sum; short Gorenstein ring; stretched Gorenstein ring; Poincaré series
associated graded ring; fibre product; connected sum; short Gorenstein ring; stretched Gorenstein ring; Poincaré series
Summary:
In 2012, Ananthnarayan, Avramov and Moore gave a new construction of Gorenstein rings from two Gorenstein local rings, called their connected sum. In this article, we investigate conditions on the associated graded ring of a Gorenstein Artin local ring $Q$, which force it to be a connected sum over its residue field. In particular, we recover some results regarding short, and stretched, Gorenstein Artin rings. Finally, using these decompositions, we obtain results about the rationality of the Poincaré series of $Q$.
References:
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