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arXiv · 1005.2375

Rationality of quotients by linear actions of affine groups

Fedor Bogomolov·Christian Böhning·Hans-Christian Graf von Bothmer
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Abstract

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.

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Fedor Bogomolov, Christian Böhning, Hans-Christian Graf von Bothmer. 2010-07-16. Rationality of quotients by linear actions of affine groups. https://doi.org/10.1007/s11425-010-4127-z

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