The depth of the Rees algebra of three general binary forms. Issue 2 (1st February 2019)

• Record Type: Journal Article
• Authors: Burity, Ricardo; Simis, Aron
• Is Part Of: Communications in algebra. Volume 47:Issue 2(2019)
• Page Start: 451
• Page End: 469
• Publication Date: 2019-02-01
• Subjects: Almost Cohen–Macaulay -- Hilbert function -- Huckaba–Marley test -- Ratliff–Rush filtration -- Rees algebra; 13A02 -- 13A30 -- 13C15 -- 13D02 -- 13D40; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2018.1477950
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: One proves that the Rees algebra of an ideal generated by three general binary forms of same degree≥ 5 has depth one. The proof hinges on the behavior of the Ratliff–Rush filtration for low powers of the ideal and on establishing that certain large matrices whose entries are quadratic forms have maximal rank. One also conjectures a shorter result that implies the main theorem of the paper.