2000/01/26 by Mircea Mustata
Mathematics · #math.AC #math.AG #math.CO #msc:13D45 #msc:13D02 #msc:13D07
published as J. Symbolic Comput. 29 (2000), no. 4-5, 709-720. · 13 pages, 2 figures, to appear in Journal of Symbolic Computation
arxiv created 2000/01/26 · arxiv updated 2009/11/30
For a reduced monomial ideal B in R=k[X1,...,Xn], we write HiB(R) as the union of Exti(R/B^[d],R)d, where B^[d]d are the "Frobenius powers of B". We describe HiB(R)p, for every p in Zn, in the spirit of the Stanley-Reisner theory. As a first application we give an isomorphism Tori(B', k)p\iso Ext|p|-i(R/B,R)-p for all p in 0,1n, where B' is the Alexander dual ideal of B. We deduce a canonical filtration of Exti(R/B,R) with succesive quotients of the form R/(Xj1,...,Xji) suitably shifted, the multiplicities being computed from the Betti numbers of B'. As a final application, we give a topological description for the associated primes of Exti(R/B,R).