BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Equivariant Hilbert Series in non-Noetherian Polynomial Rings Nagel, Uwe


Ideals in polynomial rings in countably many variables that are invariant under a suitable action of a symmetric group or the monoid of strictly increasing functions arise in various contexts. We study such an ideal using an ascending chain of invariant ideals. We establish that the associated equivariant Hilbert series is a rational function in two variables. This is used to prove that the Krull dimensions and multiplicities of ideals in such an invariant filtration grow eventually linearly and exponentially, respectively. Furthermore, we determine the terms that dominate this growth. This may also be viewed as a method for assigning new asymptotic invariants to a homogenous ideal in a noetherian polynomial ring. This is based on joint work with Tim Roemer.

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