Invariant Theory and Hilbert's 14th problem

Floriana Amicone (The University of Manchester)


The aim of Invariant Theory is to study polynomial functions which are invariant under the action of a group on a certain geometric object (a vector space or a variety, say). In many instances, finding (or at least describing) generators and relations for the ring of invariant polynomials is a very hard problem, in which the geometry of the orbits plays a crucial role. One of the main questions addressed in the past was whether for every group the ring of invariants is finitely generated. This is pretty much the formulation of Hilbert's 14th problem, that was solved a few decades ago.

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