On the Hilbert series of ideals generated by generic forms. Issue 8 (3rd August 2017)

• Record Type: Journal Article
• Authors: Nicklasson, Lisa
• Is Part Of: Communications in algebra. Volume 45:Issue 8(2017)
• Page Start: 3390
• Page End: 3395
• Publication Date: 2017-08-03
• Subjects: Graded algebras -- generic forms -- Hilbert series; 13A02 -- 13F20; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2016.1236931
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: There is a longstanding conjecture by Fröberg about the Hilbert series of the ring R ∕ I, where R is a polynomial ring, and I an ideal generated by generic forms. We prove this conjecture true in the case when I is generated by a large number of forms, all of the same degree. We also conjecture that an ideal generated by m 'th powers of generic forms of degree d ≥2 gives the same Hilbert series as an ideal generated by generic forms of degree md . We verify this in several cases. This also gives a proof of the first conjecture in some new cases.