Local Cohomology at Monomial Ideals
| dc.creator | Mustata, Mircea | |
| dc.date | 2000-01-26 | |
| dc.date.accessioned | 2026-07-07T04:33:26Z | |
| dc.date.available | 2026-07-07T04:33:26Z | |
| dc.description | For a reduced monomial ideal B in R=k[X_1,...,X_n], we write H^i_B(R) as the union of {Ext^i(R/B^[d],R)}_d, where {B^[d]}_d are the "Frobenius powers of B". We describe H^i_B(R)_p, for every p in Z^n, in the spirit of the Stanley-Reisner theory. As a first application we give an isomorphism Tor_i(B', k)_p\iso Ext^{|p|-i}(R/B,R)_{-p} for all p in {0,1}^n, where B' is the Alexander dual ideal of B. We deduce a canonical filtration of Ext^i(R/B,R) with succesive quotients of the form R/(X_{j_1},...,X_{j_i}) 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 Ext^i(R/B,R). | |
| dc.description | 13 pages, 2 figures, to appear in Journal of Symbolic Computation | |
| dc.identifier | https://arxiv.org/abs/math/0001153 | |
| dc.identifier | http://arxiv.org/abs/math/0001153 | |
| dc.identifier | J. Symbolic Comput. 29 (2000), no. 4-5, 709-720. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58577 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Combinatorics | |
| dc.subject | 13D45 (Primary); 13D02; 13D07 (Secondary) | |
| dc.title | Local Cohomology at Monomial Ideals | |
| dc.type | text |