The primary goal of this 2003 book is to give a brief introduction to the main ideas of
algebraic and geometric invariant theory. It assumes only a minimal background in algebraic …

3.1. Introduction......................................... 3.2. Connection Between Integral and Rational
Invariants...... 3.3. Basic Invariants...................................... 3.4. Hilbert's Theorem on …

Contents. Introduction. I. Representations and the geometry of homogeneous spaces. 1.
Generalities on representations. 2. Reductive groups. 3. Bruhat decompositions of …

Since the late 1960s, methods of birational geometry have been used successfully in the
theory of linear algebraic groups, especially in arithmetic problems. This book--which can be …

The invariant theory of non-reductive groups has its roots in the 19th century but has seen
some very interesting developments in the past twenty years. This book is an exposition of …

Let G be an algebraic group defined over an algebraicly closed field k.(See [1].) If k=(C, then
G is naturally a Lie group. A linear algebraic monoid is an affine, algebraic variety Μ with …

Let G be a reductive algebraic group and X an algebraic G-variety which admits a quotient it:
X→ X//G. In this article we describe several results concerning the Picard group Pic (X//G) of …

In this article we present a fundamental result due to Sumihiro. It states that every normal G-
variety X, where G is a connected linear algebraic group, is locally isomorphic to a quasi …

We say that a group acts infinitely transitively on a set if for every the induced diagonal
action of is transitive on the cartesian th power with the diagonals removed. We describe …

In this paper, firstly we calculate Picard groups of a nilpotent orbit 𝒪 in a classical complex
simple Lie algebra and discuss the properties of being ℚ-factorial and factorial for the …