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- W1964078251 abstract "We present a generalized version of classical geometric invariant theory à la Mumford where we consider an affine algebraic group G acting on a specific affine algebraic variety X. We define the notions of linearly reductive and of unipotent action in terms of the G fixed point functor in the category of (G, 𝕜[X])-modules. In the case that X = {⋆} we recuperate the concept of linearly reductive and of unipotent group. We prove in our relative context some of the classical results of GIT such as: existence of quotients, finite generation of invariants, Kostant–Rosenlicht's theorem and Matsushima's criterion. We also present a partial description of the geometry of such linearly reductive actions." @default.
- W1964078251 created "2016-06-24" @default.
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- W1964078251 date "2015-05-01" @default.
- W1964078251 modified "2023-09-26" @default.
- W1964078251 title "Linearly reductive and unipotent actions of affine groups" @default.
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- W1964078251 doi "https://doi.org/10.1142/s0129167x15500317" @default.
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