Rationality of quotients by linear actions of affine groups

Details Rationality of quotients by linear actions of affine groups Rationality of quotients by linear actions of affine groups

2010-05-13

arxiv.org/abs/1005.2375v2

Mathematics

Algebraic Geometry

18 pages; dedicated to Fabrizio Catanese on the occasion of his 60th birthday

Scientific paper

10.1007/s11425-010-4127-z

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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