Knop, Friedrich Der kanonische Modul eines Invariantenrings. (The canonical module of a ring of invariants). (German) Zbl 0716.20021 J. Algebra 127, No. 1, 40-54 (1989). 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. Cited in 2 ReviewsCited in 18 Documents 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.) Keywords:canonical module; ring of invariants; reductive group; affine variety; generating function PDF BibTeX XML Cite \textit{F. Knop}, J. Algebra 127, No. 1, 40--54 (1989; Zbl 0716.20021) Full Text: DOI OpenURL References: [1] Boutot, J.-F, Singularités rationelles et quotients par LES groupes réductifs, Invent. math., 88, 65-68, (1987) · Zbl 0619.14029 [2] Hartshorne, R, Stable reflexive sheaves, Math. ann., 254, 121-176, (1980) · Zbl 0431.14004 [3] () [4] Hochster, M; Roberts, J, Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay, Adv. in math., 13, 115-175, (1974) · Zbl 0289.14010 [5] Kempf, G, The hochster-Roberts theorem in invariant theory, Michigan math. J., 26, 19-32, (1979) · Zbl 0409.13004 [6] Knop, F, Über die glattheit von quotientenabbildungen, Manuscripta math., 56, 419-427, (1986) · Zbl 0585.14033 [7] Knop, F; Littelmann, P, Der Grad erzeugender funktionen von invariantenringen, Math. Z., 196, 211-231, (1987) · Zbl 0635.20017 [8] Luna, D, Slices étales, Bull. soc. math. France, 33, 81-105, (1973) · Zbl 0286.14014 [9] Luna, D; Richardson, R.W, A generalization of the Chevalley restriction theorem, Duke math. J., 46, 487-496, (1976) · Zbl 0444.14010 [10] Popov, V.L, The constructive theory of invariants, Math. USSR-izv., 19, 359-376, (1982) · Zbl 0501.14006 [11] Raynaud, M; Gruson, L, Critères de platitude et de projectivité. techniques de “platification” d’un module, Invent. math., 13, 1-89, (1971) · Zbl 0227.14010 [12] Stanley, R, Hilbert functions of graded algebras, Adv. in math., 28, 57-83, (1978) · Zbl 0384.13012 [13] Stanley, R, Combinatorics and commutative algebras, () [14] Watanabe, K, Certain invariant subrings are Gorenstein, I. Osaka J. math., 11, 1-8, (1974) · Zbl 0281.13007 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.