“Geometric Invariant Theory” by Mumford/Fogarty (the first edition was published in 1965, a
second, enlarged edition appeared in 1982) is the standard reference on applications of …

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 …

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 …

This is a survey on the ancient question: Let G be a reductive group over an algebraically
closed field k and let V be a vector space over k with an almost free linear action of G on V …

Observe that rank ox< 1. Consider the open set Eo={xc Elrankilx= 1}. If x E Eo, then E is
smooth at x and E= E1 near x. The following construction will show that Eo is non …

We introduce and study the notion of essential dimension for linear algebraic groups defined
over an algebraically closed fields of characteristic zero. The essential dimension is a …

We apply classical invariant theory of binary forms to explicitly characterize isomorphism
classes of hyperelliptic curves of small genus and, conversely, propose algorithms for …

We give the first examples of finite groups G such that the Chow ring of the classifying space
BG depends on the base field, even for fields containing the algebraic closure of ℚ. As a …

In this paper we consider Gorenstein stable surfaces with and positive geometric genus.
Extending classical results, we show that such surfaces admit a simple description as …