Abstract
Consider the action of a group G ≤ Sn that permutes the n variables in a polynomial ring k[X1,...,Xn] over a field k. Two related properties, the Cohen-Macaulay property and F-rationality, are studied in the ring of invariants, and the following results are obtained. (1) The invariant ring k[X1,...,Xn]Cn produced by cyclic permutation of the variables is shown not to be Cohen-Macaulay in characteristics dividing n for n > 4. This completes the analysis of the characteristics in which this invariant ring is Cohen-Macaulay. (2) The non-F-rational locus of k[X1,...,Xn]An is found to have positive dimension for certain n and k, although this ring possesses many of the properties of F-rational rings.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
