Limit points and additive group actions

Rational Fixed Points for Linear Group Actions

Pietro Corvaja §1 Introduction. A general principle in the theory of diophantine equations asserts that if an equation admits " many " rational solutions, there should be a geometric reason explaining such abundance. We consider here a (multiplicative) semigroup of N ×N matrices with rational entries: we suppose that all of them admit rational eigenvalues and deduce the natural geometrical cons...

Separating Invariants for Arbitrary Linear Actions of the Additive Group

We consider an arbitrary representation of the additive group Ga over a field of characteristic zero and give an explicit description of a finite separating set in the corresponding ring of invariants.

Group Actions and Group Extensions

In this paper we study finite group extensions represented by special cohomology classes. As an application, we obtain some restrictions on finite groups which can act freely on a product of spheres or on a product of real projective spaces. In particular, we prove that if (Z/p)r acts freely on (S1)k , then r ≤ k.

Singularities and Group Actions

Group Actions

The symmetric groups Sn, alternating groups An, and (for n ≥ 3) dihedral groups Dn behave, by their very definition, as permutations on certain sets. The groups Sn and An both permute the set {1, 2, . . . , n} and Dn can be considered as a group of permutations of a regular n-gon, or even just of its n vertices, since rigid motions of the vertices determine where the rest of the n-gon goes. If ...