Codes and Expansions (CodEx) Seminar

Mátyás Domokos (Alfréd Rényi Institute of Mathematics):
Degree bounds for separating invariants

A common situation in mathematics is that we are given an action of a group on a finite dimensional vector space, and we would like to have an effective way to decide whether two vectors belong to the same orbit or not. The algebraic approach leads to the search for generators of the corresponding algebra of polynomial invariants (i.e. polynomial functions on the vector space that are constant along the orbits). Although finding all the generators is essential for constructing appropriate quotient varieties in the context of algebraic geometry, determining a so-called separating set of polynomial invariants is just as good from the point of view of the orbit separation problem, whose solution is after all the main aim in several applications. In the talk we shall first survey some trends in the study of separating sets in invariant theory, and then we turn to the following question: is the switch from the notion of 'generating sets' to the more general notion of 'separating sets' reflected in degree bounds?