Graded Betti Numbers of the Logarithmic Derivation Module
| dc.creator | Marco-Buzunariz, Miguel Ángel | |
| dc.creator | Martín-Morales, Jorge | |
| dc.date | 2009-04-22 | |
| dc.date.accessioned | 2026-07-07T13:07:18Z | |
| dc.date.available | 2026-07-07T13:07:18Z | |
| dc.description | Let $Q\in \K[x_1,...,x_n] = S$ be a homogeneous polynomial of degree $d$. The freeness of the logarithmic derivation module, $D(Q)$, and of its natural generalizations, has been widely studied. In the free case, $D(Q) \simeq \bigoplus_{i=1}^n S(-d_i)$ where the $d_i$'s are the exponents of the module; and as a direct consequence of the Saito-Ziegler criterion, the formula $d = \sum_i d_i$ holds. In this paper we give a generalization of this formula in the non-free case. Moreover, we show that an equivalent formula is also true in the quasi-homogeneous case, and show to what extent it can be generalized for arbitrary polynomials. | |
| dc.identifier | https://arxiv.org/abs/0904.3465 | |
| dc.identifier | http://arxiv.org/abs/0904.3465 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/228045 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13N15; 32S25 | |
| dc.title | Graded Betti Numbers of the Logarithmic Derivation Module | |
| dc.type | text |