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Der kanonische Modul eines Invariantenrings. (The canonical module of a ring of invariants). (German) Zbl 0716.20021

Summary: We calculate the canonical module of a ring of invariants R of a reductive group acting on an affine variety. From that we derive a criterion for the Gorenstein property to hold for R. In case R is the ring of invariants of a graded ring we obtain lower and upper bounds for the degree of the generating function of R.

MSC:

20G05 Representation theory for linear algebraic groups
14L30 Group actions on varieties or schemes (quotients)
14L24 Geometric invariant theory
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
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