Invariant theory

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• ID : Q1855669

말뭉치

1. Turnbull’s work on invariant theory built on the symbolic methods of the German mathematicians Rudolf Clebsch (1833-1872) and Paul Gordan (1837-1912).
2. This paper presents a simple graphical method, closely related to the “algebrochemical method” of Clifford and Sylvester, for computations in the classical invariant theory of binary forms.
3. One of the first objects of study in invariant theory were the so-called invariants of forms.
4. Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties, such as vector spaces, from the point of view of their effect on functions.
5. Modern research in invariant theory of finite groups emphasizes "effective" results, such as explicit bounds on the degrees of the generators.
6. Invariant theory of infinite groups is inextricably linked with the development of linear algebra, especially, the theories of quadratic forms and determinants.
7. Another subject with strong mutual influence was projective geometry, where invariant theory was expected to play a major role in organizing the material.
8. A uniform formulation, applying to all classical groups simultaneously, of the First Fundamental Theory of Classical Invariant Theory is given in terms of the Weyl algebra.
9. Classically, invariant theory studies orbits under group actions, orbit closures, and the equations that vanish on them.
10. These invariant theory structures were studied classically by mathematicians including David Hilbert and Emmy Noether.
11. This picture describes our invariant theory set-up.
12. Invariant theory is a classical subject whose history is deeply intertwined with the foundations of algebraic geometry.
13. The core topic will be geometric invariant theory, but aspects of computational invariant theory, and what might be termed arithmetic invariant theory will also be explored.
14. Geometric invariant theory is an essential tool for constructing moduli spaces in algebraic geometry, but there are many moduli problems which do not neatly fit into this framework.
15. Recently a theory has emerged which treats the results and structures of geometric invariant theory in a broader context.
16. The general equivalence is demonstrated, so far as elementary applications are concerned, of the method of tensors with the classical symbolic method of invariant theory.
17. Part III consists of applications to the classical problems of invariant theory.
18. Geometric Invariant Theory was developed by Mumford to construct quotients in algebraic geometry.
19. So my question is pretty much summed up by the summary - basically I've run into a need to teach myself some of the basics of invariant theory and was looking for a good place to start.
20. The book starts with an introduction to Geometric Invariant Theory (GIT).
21. That this is actually the case is one of the main results of Hilbert’s landmark paper of 1890, a paper which would be the cause of the “first demise” of invariant theory.

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위키데이터

• ID : Q1855669