In this article we review the question of constructing geometric quotients of actions of linear
algebraic groups on irreducible varieties over algebraically closed fields of characteristic …

Degree bounds for algebra generators of invariant rings are a topic of longstanding interest
in invariant theory. We study the analogous question for field generators for the field of …

The main purpose of this paper is to give a survey of algorithms in invariant theory, with
emphasis on nonreductive groups and on recent developments. But the article has some …

The first part of this paper is a refinement of Winkelmann's work on invariant rings and
quotients of algebraic group actions on affine varieties, where we take a more geometric …

Given an action of an affine algebraic group with only trivial characters on a factorial variety,
we ask for categorical quotients. We characterize existence in the category of algebraic …

For a group G acting on an affine variety X, the separating variety is the closed subvariety of
X× X encoding which points of X are separated by invariants. We concentrate on the …

In this thesis we develop a framework for constructing quotients of varieties by actions of
linear algebraic groups which is similar in spirit to that of Mumford's geometric invariant …

Given an action of an affine algebraic group with only trivial characters on a factorial variety,
we ask for categorical quotients. We characterize existence in the category of algebraic …

Throughout this section G will be a linearly reductive group over an algebraically closed field
K and V will be an n-dimensional rational representation. We will present an algorithm for …