Abstract
We consider varieties over an algebraically closed field k of characteristicp>0. Given a linear representation of a reductive group, we prove that the ring of invariants is F-regular provided the associated projective quotient is Frobenius-split, the twisting sheaves are Cohen-Macaulay (C-M), and a mild technical condition is met. As an example of how this can be used, we show that the ring of invariants (under the adjoint action of SL (3)) ofg copies ofM 3 is C-M. (HereM 3 denotes the vector space of 3×3 matrices over k andp>3.) The method of proof involves an induction, and is potentially of wide applicability. As a corollary we obtain that the moduli space of rank 3 and degree 0 bundles on a smooth projective curve of genusg is C-M.
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We thank the referees for their patient reading of the manuscript and suggestions regarding the exposition.
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Mehta, V.B., Ramadas, T.R. Frobenius splitting and invariant theory. Transformation Groups 2, 183–195 (1997). https://doi.org/10.1007/BF01235940
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DOI: https://doi.org/10.1007/BF01235940