Schmitt - Geometric Invariant Theory and Decorated Principal Bundles: this might also be interesting if you are interested in the geometric applications and the related geometry, though I haven't looked into this book very much, but Part 1 does contain a fairly leisurely-looking introduction to GIT.

There is also Popov's and Vinberg's treatise "Invariant Theory" in the Ecyclopedia of Mathematical Sciences Volume 55 Springer which contains a good summary of the classical results in characteristic zero. I would recommend a look at chapter 8 of the third edition of Geometric invariant theory by Mumford, Forgarty and Kirwan.

It describes a connection between GIT and Hamiltonian group actions in symplectic geometry. The Hilbert schema chapter is very important need the Hartshorne "Algebraic Geometry" as base.

Or in more gentle way: Fundamental Algebraic Geometry. Read the survey in my article and go over the references therein.

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## Applications of Invariant Theory

Viewed 3k times. At the very least, I think the OP should clarify more carefully what is his background in presumably complex differential geometry, and precisely how far along he is in learning algebraic geometry. Schmitt - Geometric Invariant Theory and Decorated Principal Bundles: this might also be interesting if you are interested in the geometric applications and the related geometry, though I haven't looked into this book very much, but Part 1 does contain a fairly leisurely-looking introduction to GIT There is also Popov's and Vinberg's treatise "Invariant Theory" in the Ecyclopedia of Mathematical Sciences Volume 55 Springer which contains a good summary of the classical results in characteristic zero.

Jason Polak Jason Polak 1, 1 1 gold badge 12 12 silver badges 25 25 bronze badges. Eugene Lerman Eugene Lerman 1, 8 8 silver badges 14 14 bronze badges.

Fogarty J. Buschi Sergio Buschi Sergio 2, 1 1 gold badge 16 16 silver badges 23 23 bronze badges. Sorry could not resist. In the second part, chapters two to six, and to treat the case of finite characteristic, the authors develop the theory of quasi-hereditary algebras, using combinatorial methods when needed, to avoid the original deep methods of the algebraic geometry of line bundles on flag varieties.

The first fundamental theorem is proved in chapter four and the second fundamental theorem in chapter five. The choices made by the authors permit them to highlight the main results and also to keep the material within the reach of an interested reader. At the same time the book remains open-ended, with precise pointers to the literature on other approaches and the cases not treated here. His e-mail address is fz xanum.

## The Invariant Theory of Matrices | Mathematical Association of America

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