2020/07/30 by A. V. Jayanthan, Arvind Kumar, Jayanthan, A. V. +1
Mathematics · #05E40 #13D02 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:05E40 #msc:13D02
paper · pdf · doi:10.48550/arxiv.2007.15319
23 pages, Comments are welcome
arxiv created 2020/07/30 · arxiv updated 2020/07/31
Let R = \mathbbK[x1, …, xn] and I ⊂ R be a homogeneous ideal. In this article, we first obtain certain sufficient conditions for the subadditivity of R/I. As a consequence, we prove that if I is generated by homogeneous complete intersection, then subadditivity holds for R/I. We then study a conjecture of Avramov, Conca and Iyengar on subadditivity, when I is a monomial ideal with R/I Koszul. We identify several classes of edge ideals of graphs G such that the subadditivity holds for R/I(G). We then study the strand connectivity of edge ideals and obtain several classes of graphs whose edge ideals are strand connected. Finally, we compute upper bounds for multigraded Betti numbers of several classes of edge ideals.