Betti numbers of Koszul algebras defined by four quadrics

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:225

Article

Mantero, Paolo¹  Mastroeni, Matthew² 

[1] Univ Arkansas, Dept Math, Fayetteville, AR 72701 USA

[2] Oklahoma State Univ, Dept Math, Stillwater, OK 74078 USA

关键词: Betti numbers;    Koszul algebras;    Projective dimension;   

DOI  :  10.1016/j.jpaa.2020.106504

来源: Elsevier

【 摘 要 】

Let I be an ideal generated by quadrics in a standard graded polynomial ring S over a field. A question of Avramov, Conca, and Iyengar asks whether the Betti numbers of R = S/I over S can be bounded above by binomial coefficients on the minimal number of generators of I if R is Koszul. This question has been answered affirmatively for Koszul algebras defined by three quadrics and Koszul almost complete intersections with any number of generators. We give a strong affirmative answer to the above question in the case of four quadrics by completely determining the Betti tables of height two ideals of four quadrics defining Koszul algebras. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free