2021/12/29 by Anthony Iarrobino, Iarrobino, Anthony, Pedro Macías Marques +1
Chemistry · Mathematics · #13H10 (Primary) 13E10 #14B07 #14C05 (Secondary) #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Oxidative Organic Chemistry Reactions
paper · pdf · doi:10.48550/arxiv.2112.14664
openalex publication_date 2021/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Jordan type of an Artinian algebra is the Jordan block partition associated to multiplication by a generic element of the maximal ideal. We study the Jordan type for Artinian Gorenstein (AG) local algebras A, and the interaction of Jordan type with the symmetric decomposition of the Hilbert function H(A). We give examples of Gorenstein sequences H for which the family Gor(H) of AG algebras having Hilbert function H has several irreducible components, each corresponding to a symmetric decomposition of H. The component structure results from the intersection of two opposing filtrations of the family Gor(H) of AG algebras: that by Jordan type satisfies the usual dominance property; the second filtration, by symmetric decomposition, satisfies a known semicontinuity property. Our examples are in codimension three -- the lowest codimension of such an example, as Gor(H) is irreducible in codimension two.