Bounds for the multiplicity of Gorenstein algebras

El Khoury, Sabine; Kummini, Manoj; Srinivasan, Hema

doi:10.1090/S0002-9939-2014-12275-1

Bounds for the multiplicity of Gorenstein algebras
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by Sabine El Khoury, Manoj Kummini and Hema Srinivasan PDF

Proc. Amer. Math. Soc. 143 (2015), 121-128 Request permission

Abstract:

We prove upper bounds for the Hilbert-Samuel multiplicity of standard graded Gorenstein algebras. The main tool that we use is Boij-Söderberg theory to obtain a decomposition of the Betti table of a Gorenstein algebra as the sum of rational multiples of symmetrized pure tables. Our bound agrees with the one in the quasi-pure case obtained by Srinivasan [J. Algebra, vol. 208, no. 2 (1998)].

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