Intersections of Leray complexes and regularity of monomial ideals
| dc.creator | Kalai, Gil | |
| dc.creator | Meshulam, Roy | |
| dc.date | 2006-01-30 | |
| dc.date.accessioned | 2026-07-07T06:59:30Z | |
| dc.date.available | 2026-07-07T06:59:30Z | |
| dc.description | For a simplicial complex X and a field K, let h_i(X)=\dim \tilde{H}_i(X;K). It is shown that if X,Y are complexes on the same vertex set, then for all k h_{k-1}(X\cap Y) \leq \sum_{σ\in Y} \sum_{i+j=k} h_{i-1}(X[σ])\cdot h_{j-1}(\lk(Y,σ)) . A simplicial complex X is d-Leray over K, if h_i(Y)=0 for all induced subcomplexes Y \subset X and i \geq d. Let L_K(X) denote the minimal d such that X is d-Leray over K. The above theorem implies that if X,Y are simplicial complexes on the same vertex set then L_K(X \cap Y) \leq L_K(X) +L_K(Y). Reformulating this inequality in commutative algebra terms, we obtain the following result conjectured by Terai: If I,J are square-free monomial ideals in S=K[x_1,...,x_n], then reg(I+J) \leq reg(I)+reg(J)-1 where reg(I) denotes the Castelnuovo-Mumford regularity of I. | |
| dc.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/math/0601745 | |
| dc.identifier | http://arxiv.org/abs/math/0601745 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107771 | |
| dc.subject | Combinatorics | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13F55; 55U10 | |
| dc.title | Intersections of Leray complexes and regularity of monomial ideals | |
| dc.type | text |