Analytic isomorphisms of compressed local algebras
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- by J. Elias and M. E. Rossi PDF
- Proc. Amer. Math. Soc. 143 (2015), 973-987 Request permission
Abstract:
In this paper we consider Artin compressed local algebras, that is, local algebras with maximal length in the class of those with given embedding dimension and socle type. They have been widely studied by several authors, including Boij, Iarrobino, Fröberg and Laksov. In this class the Gorenstein algebras play an important role. The authors proved that a compressed Gorenstein $K$-algebra of socle degree $3$ is canonically graded, i.e. analytically isomorphic to its associated graded ring. This unexpected result has been extended to compressed level $K$-algebras of socle degree $3$ in a paper by De Stefani. This paper somehow concludes the investigation proving that Artin compressed Gorenstein $K$-algebras of socle degree $s \le 4$ are always canonically graded, but explicit examples prove that the result does not extend to socle degree $5$ or to compressed level $K$-algebras of socle degree $4$ and type $>1.$ As a consequence of this approach we present classes of Artin compressed $K$-algebras which are canonically graded.References
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Additional Information
- J. Elias
- Affiliation: Departament d’Àlgebra i Geometria, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain
- MR Author ID: 229646
- ORCID: 0000-0003-3053-1542
- Email: elias@ub.edu
- M. E. Rossi
- Affiliation: Dipartimento di Matematica, Università di genova, Via Dodecaneso 35, 16146 Genova, Italy
- MR Author ID: 150830
- ORCID: 0000-0001-7039-5296
- Email: rossim@dima.unige.it
- Received by editor(s): August 6, 2012
- Received by editor(s) in revised form: July 2, 2013
- Published electronically: November 5, 2014
- Additional Notes: The first author was partially supported by MTM2013-40775-P
The second author was partially supported by PRIN 2010-11 “Geometria delle varieta’ algebriche” - Communicated by: Irena Peeva
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 973-987
- MSC (2010): Primary 13H10; Secondary 13H15, 14C05
- DOI: https://doi.org/10.1090/S0002-9939-2014-12313-6
- MathSciNet review: 3293715