2024/04/10 by H. Ananthnarayan, Omkar Javadekar, Ananthnarayan, H. +3
Mathematics · #13A02 #13D02 #13D40 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2404.07297
openalex publication_date 2024/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let R be a fibre product of standard graded algebras over a field. We study the structure of syzygies of finitely generated graded R-modules. As an application of this, we show that the existence of an R-module of finite regularity and infinite projective dimension forces R to be Koszul. We also look at the extremal rays of the Betti cone of finitely generated graded R-modules, and show that when depth(R)=1, they are spanned by the Betti tables of pure R-modules if and only if R is Cohen-Macaulay with minimal multiplicity.