• The Poincaré Series of a Local Gorenstein Ring of Multiplicity up to 10 is Rational

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    • Keywords


      Gorenstein; Artinian; Poincaré series.

    • Abstract


      Let 𝑅 be a local, Gorenstein ring with algebraically closed residue field 𝑘 of characteristic 0 and let $P_R(z):=\sum^\infty_{p=0}\dim_k(\mathrm{Tor}^R_p(k, k))z^p$ be its Poincaré series. We compute $P_R$ when 𝑅 belongs to a particular class defined in the Introduction, proving its rationality. As a by-product we prove the rationality of $P_R$ for all local, Gorenstein rings of multiplicity at most 10.

    • Author Affiliations


      Gianfranco Casnati1 2 Roberto Notari1 2

      1. Dipartimento di Matematica, Politecnico di Torino, c.so Duca degli Abruzzi 24, 10129 Torino, Italy
      2. Dipartimento di Matematica “Francesco Brioschi”, Politecnico di Milano, via Bonardi 9, 20133 Milano, Italy
    • Dates

  • Proceedings – Mathematical Sciences | News

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      Posted on July 25, 2019

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