Degrees of Regular Sequences With a Symmetric Group Action. (7th January 2019)

• Record Type: Journal Article
• Authors: Galetto, Federico; Geramita, Anthony Vito; Wehlau, David Louis
• Is Part Of: Canadian journal of mathematics. Volume 71:Number 3(2019)
• Page Start: 557
• Page End: 578
• Publication Date: 2019-01-07
• Subjects: 13A02, -- 13A50, -- 20C30; complete intersection, -- symmetric group, -- regular sequence; Mathematics -- Periodicals; Mathematics; Electronic journals; Periodicals; 510
• DOI: 10.4153/CJM-2017-035-3
• Languages: English
• ISSNs: 0008-414X

Abstract

Abstract: We consider ideals in a polynomial ring that are generated by regular sequences of homogeneous polynomials and are stable under the action of the symmetric group permuting the variables. In previous work, we determined the possible isomorphism types for these ideals. Following up on that work, we now analyze the possible degrees of the elements in such regular sequences. For each case of our classification, we provide some criteria guaranteeing the existence of regular sequences in certain degrees.