On simple A-multigraded minimal resolutions
| dc.creator | Charalambous, Hara | |
| dc.creator | Thoma, Apostolos | |
| dc.date | 2009-01-09 | |
| dc.date.accessioned | 2026-07-07T12:27:59Z | |
| dc.date.available | 2026-07-07T12:27:59Z | |
| dc.description | Let $A$ be a semigroup whose only invertible element is 0. For an $A$-homogeneous ideal we discuss the notions of simple $i$-syzygies and simple minimal free resolutions of $R/I$. When $I$ is a lattice ideal, the simple 0-syzygies of $R/I$ are the binomials in $I$. We show that for an appropriate choice of bases every $A$-homogeneous minimal free resolution of $R/I$ is simple. We introduce the gcd-complex $D_{gcd}(\bf b)$ for a degree $\mathbf{b}\in \A$. We show that the homology of $D_{gcd}(\bf b)$ determines the $i$-Betti numbers of degree $\bf b$. We discuss the notion of an indispensable complex of $R/I$. We show that the Koszul complex of a complete intersection lattice ideal $I$ is the indispensable resolution of $R/I$ when the $A$-degrees of the elements of the generating $R$-sequence are incomparable. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/0901.1196 | |
| dc.identifier | http://arxiv.org/abs/0901.1196 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/215398 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 13D02, 13D25 | |
| dc.title | On simple A-multigraded minimal resolutions | |
| dc.type | text |