Publisher description for Geometric invariant theory / D. Mumford, J. Fogarty, F. Kirwan.
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"Geometric Invariant Theory" by Mumford/Fogarty (the first
edition was published in 1965, a second, enlarged editon
appeared in 1982) is the standard reference on applications
of invariant theory to the construction of moduli spaces.
This third, revised edition has been long awaited for by the
mathematical community. It is now appearing in a completely
updated and enlarged version with an additional chapter on
the moment map by Prof. Frances Kirwan (Oxford) and a fully
updated bibliography of work in this area.
The book deals firstly with actions of algebraic groups on
algebraic varieties, separating orbits by invariants and
constructionquotient spaces; and secondly with applications
of this theory to the construction of moduli spaces.
It is a systematic exposition of the geometric aspects of
the classical theory of polynomial invariants.
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