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Bounds for the multiplicity of Gorenstein algebras


Authors: Sabine El Khoury, Manoj Kummini and Hema Srinivasan
Journal: Proc. Amer. Math. Soc. 143 (2015), 121-128
MSC (2010): Primary 13D02, 13D40
DOI: https://doi.org/10.1090/S0002-9939-2014-12275-1
Published electronically: September 19, 2014
MathSciNet review: 3272737
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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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Additional Information

Sabine El Khoury
Affiliation: Department of Mathematics, American University of Beirut, Beirut, Lebanon
Email: se24@aub.edu.lb

Manoj Kummini
Affiliation: Chennai Mathematical Institute, Siruseri, Tamilnadu 603103, India
Email: mkummini@cmi.ac.in

Hema Srinivasan
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email: srinivasanh@missouri.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-12275-1
Keywords: Hilbert-Samuel multiplicity, graded Betti numbers, Gorenstein rings.
Received by editor(s): November 6, 2012
Received by editor(s) in revised form: May 4, 2013
Published electronically: September 19, 2014
Additional Notes: The first author thanks the American University of Beirut for supporting part of this work through a long-term development grant, and the Mathematical Sciences Research Institute, Berkeley, California, for its hospitality
The seocnd author thanks MSRI for support during Fall 2012. In addition, the first and second authors thank the University of Missouri, Columbia for its hospitality
The third author gratefully acknowledges support from MU Research Council grants and MSRI
Communicated by: Irena Peeva
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.