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Creators/Authors contains: "Şega, Liana"

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  1. ; (, Proceedings of the American Mathematical Society)
    In this article we study base change of Poincaré series along a quasi-complete intersection homomorphism φ<#comment/> :<#comment/> Q →<#comment/> R \varphi \colon Q \to R , where Q Q is a local ring with maximal ideal m \mathfrak {m} . In particular, we give a precise relationship between the Poincaré series P M Q ( t ) \mathrm {P}^Q_M(t) of a finitely generated R R -module M M to P M R ( t ) \mathrm {P}^R_M(t) when the kernel of φ<#comment/> \varphi is contained in m a n n Q ( M ) \mathfrak {m}\,\mathrm {ann}_Q(M) . This generalizes a classical result of Shamash for complete intersection homomorphisms. Our proof goes through base change formulas for Poincaré series under the map of dg algebras Q →<#comment/> E Q\to E , with E E the Koszul complex on a minimal set of generators for the kernel of φ<#comment/> \varphi . 
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    Free, publicly-accessible full text available January 1, 2026
  2. ; ; (, Transactions of the American Mathematical Society)
    We introduce the class of principal symmetric ideals, which are ideals generated by the orbit of a single polynomial under the action of the symmetric group. Fixing the degree of the generating polynomial, this class of ideals is parametrized by points in a suitable projective space. We show that the minimal free resolution of a principal symmetric ideal is constant on a non-empty Zariski open subset of this projective space and we determine this resolution explicitly. Along the way, we study two classes of graded algebras which we term narrow and extremely narrow; both of which are instances of compressed artinian algebras. 
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    Free, publicly-accessible full text available December 30, 2025