This book is about the computational aspects of invariant theory. Of central interest is the
question how the invariant ring of a given group action can be calculated. Algorithms for this …

IfVis a faithful module for a finite groupGover a field of characteristicp, then the ring of
invariants need not be Cohen–Macaulay ifpdivides the order ofG. In this article the …

This is the second volume of the new subseries" Invariant Theory and Algebraic
Transformation Groups". The aim of the survey by A. Bialynicki-Birula is to present the main …

Let KΩVä G be the invariant ring of a finite linear group G e GL Vfi, and let GU be the
pointwise stabilizer of a subspace U e V. We prove that the following numbers associated to …

Let G be a finite group acting linearly on a vector space V over a field K of positive
characteristic p and let P≤ G be a Sylow p-subgroup. Ellingsrud and Skjelbred [Compositio …

In the case of finite groups, a separating algebra is a subalgebra of the ring of invariants
which separates the orbits. Although separating algebras are often better behaved than the …

Like the Arabian phoenix rising out of the ashes, the theory of invariants, pronounced dead
at the turn of the century, is once again at the forefront of mathematics. During its long …

Let be a finite-dimensional-module over a field,, of characteristic. The maximum degree of
an indecomposable element of the algebra of invariants,, is called the Noether number of …

We classify all n-dimensional reduced Cohen-Macaulay modular quotient varieties AF n/C 2
p and study their singularities, where p is a prime number and C 2 p denotes the cyclic …

The aim of this survey is to present the main trends and directions of research in the theory
of quotients by group actions. The theory, in the assumed here sense, contains Geometric …