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Title: Artinian Gorenstein algebras of embedding dimension four and socle degree three
Authors: Macias Marques, Pedro
Veliche, Oana
Weyman, Jerzy
Keywords: Artinian Gorenstein algebra
Macaulay inverse system
Free resolution
Connected sum
Issue Date: 2023
Publisher: Journal of Algebra
Citation: Pedro Macias Marques, Oana Veliche, Jerzy Weyman, Artinian Gorenstein algebras of embedding dimension four and socle degree three, Journal of Algebra, Volume 638, 2024, Pages 788-839, ISSN 0021-8693,
Abstract: We prove that in the polynomial ring ${Q=\kk[x,y,z,w]}$, with $\kk$ an algebraically closed field of characteristic zero, all Gorenstein homogeneous ideals $I$ such that $(x,y,z,w)^4\subseteq I \subseteq (x,y,z,w)^2$ can be obtained by \emph{doubling} from a grade three perfect ideal $J\subset I$ such that $Q/J$ is a locally Gorenstein ring. Moreover, a graded minimal free resolution of the \mbox{$Q$-module} $Q/I$ can be completely described in terms of a graded minimal free resolution of the \mbox{$Q$-module} $Q/J$ and a homogeneous embedding of a shift of the canonical module $\omega_{Q/J}$ into $Q/J$.
Type: article
Appears in Collections:MAT - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica

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