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Rationality of quotients by linear actions of affine groups

Let G be the (special) affine group, semidirect product of SL_n and C^n. In this paper we study the representation theory of G and in particular the question of rationality for V/G where V is a generically free G-representation. We show that the answer to this question is positive if the dimension of V is sufficiently large and V is indecomposable. We have a more precise theorem if V is a two-step extension 0 -> S -> V -> Q -> 0 with S, Q completely reducible.

preprint2010arXivOpen access
Fedor BogomolovChristian BöhningHans-Christian Graf von Bothmer
math.AG
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Fedor BogomolovChristian BöhningHans-Christian Graf von Bothmer

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