Relative Invariants, Ideal Classes and Quasi-Canonical Modules of\n Modular Rings of Invariants

2010/11/23 by Peter Fleischmann, Fleischmann, Peter, Chris Woodcock +1 · 1 citation
Mathematics · #13B05 #13B40 #20C05 (Secondary) #20C20 (Primary) #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1011.5153

openalex publication_date 2010/11/23 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We describe "quasi canonical modules" for modular invariant rings R of\nfinite group actions on factorial Gorenstein domains. From this we derive a\ngeneral "quasi Gorenstein criterion" in terms of certain 1-cocycles. This\ngeneralizes a recent result of A. Braun for linear group actions on polynomial\nrings, which itself generalizes a classical result of Watanabe for non-modular\ninvariant rings.\n We use an explicit classification of all reflexive rank one R-modules,\nwhich is given in terms of the class group of R, or in terms of\nR-semi-invariants. This result is implicitly contained in a paper of Nakajima\n( citeNakajima:rel_inv).\n

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