The Hilbert Function of a Maximal Cohen-Macaulay Module
| dc.creator | Puthenpurakal, Tony J. | |
| dc.date | 2004-09-03 | |
| dc.date | 2005-01-31 | |
| dc.date.accessioned | 2026-07-07T05:11:46Z | |
| dc.date.available | 2026-07-07T05:11:46Z | |
| dc.description | We study Hilbert functions of maximal Cohen-Macaulay(=CM) modules over CM local rings. We show that if $A$ is a hypersurface ring with dimension $d > 0$ then the Hilbert function of $M$ \wrt $\m$ is non-decreasing. If $A = Q/(f)$ for some regular local ring $Q$, we determine a lower bound for $e_0(M)$ and $e_1(M)$. We analyze the case when equality holds and prove that in this case $G(M)$ is CM. Furthermore in this case we also determine the Hilbert function of $M$. When $A$ is Gorenstein then $M$ is the first syzygy of $S^A(M) = (\Syz^{A}_{1}(M^*))^*$. A relation between the second Hilbert coefficient of $M$, $A$ and $S^A(M)$ is found when $G(M)$ is \CM and $\depth G(A) \geq d-1$. We give bounds for the first Hilbert coefficients of the canonical module of a CM local ring and analyse when equality holds. We also give good bounds on Hilbert coefficients of $M$ when $M$ is maximal CM and $G(M)$ is CM. | |
| dc.description | referee's suggestions added, 20 pages, accepted for publication in Math Z | |
| dc.identifier | https://arxiv.org/abs/math/0409051 | |
| dc.identifier | http://arxiv.org/abs/math/0409051 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72358 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13D40 | |
| dc.title | The Hilbert Function of a Maximal Cohen-Macaulay Module | |
| dc.type | text |