Seminar

The Poincare series of a finitely generated module over a commutative local ring is defined to be the generating series of its Betti numbers. Although examples of rings with transcendental Poincare series exist, there seems to be an abundance of rings for which the Poincare series of all finitely generated modules are rational, sharing a common denominator. I will present recent work with Marilina Rossi, in which we prove that this property holds for generic Gorenstein Artinian algebras. When the socle degree is different than 3, this property holds more generally, for all local Artinian rings whose associated graded algebra is Gorenstein and has extremal (compressed) Hilbert series.