On Hilbert functions and H-vectors of graded modules for finite sets of points in projective space
| dc.contributor.author | Mgani, Damas Karmel | |
| dc.date.accessioned | 2021-10-17T18:38:32Z | |
| dc.date.available | 2021-10-17T18:38:32Z | |
| dc.date.issued | 2018 | |
| dc.description | Available in print form, Eat Africana Collection, Dr. Wilbert Chagula Library,(THS EAF QA150.T34M42) | en_US |
| dc.description.abstract | In this research, we study the Hilbert functions and h-vectors of graded modules with support on finite sets of points in projective space, P_k^n To attain this, we construct the graded modules from the sets of points in projective space. For example, taking X as the set of points, we define an ideal Ix to be the homogeneous ideal in R generated by all forms vanishing at all points of X, and RX: = R/Ix the homogeneous coordinate ring of X. We use a computer software package for algebraic computations Macaulay 2 to study the Hilbert functions, h-vectors and the resulting Betti diagrams of the constructed graded modules. We then concentrate on proving the following three main results. First, we prove that the degree of a homogeneous ideal J for which RX/J is Artinian is the initial degree of the minimal generator(s) of J. This is done by studying the Hilbert function of a homogeneous coordinate ring RX/J. Apart from an ideal J we construct monomial ideals I, I* ⊆ RX then we investigate the structure of the resulting quotient rings. In addition, we prove that a submodule of torsion less module is torsion less. Second, we study the relationship between h-vectors of graded modules and structure of the associated Betti diagrams. Lastly, we present some characterizations of torsion less and reflexive modules over Noetherian rings and integral domains. | en_US |
| dc.identifier.citation | Mgani, D. K. (2018) On Hilbert functions and H-vectors of graded modules for finite sets of points in projective space. Masters dissertation, University of Dar es Salaam, Dar es Salaam. | en_US |
| dc.identifier.uri | http://41.86.178.5:8080/xmlui/handle/123456789/16107 | |
| dc.language.iso | en | en_US |
| dc.publisher | University of Dar es Salaam | en_US |
| dc.subject | Algebra | en_US |
| dc.subject | graded modules | en_US |
| dc.subject | Finite group | en_US |
| dc.subject | Projective space | en_US |
| dc.subject | Tanzania | en_US |
| dc.title | On Hilbert functions and H-vectors of graded modules for finite sets of points in projective space | en_US |
| dc.type | Thesis | en_US |