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dc.contributor.authorGrieve, Nathan
dc.contributor.otherQueen's University (Kingston, Ont.). Theses (Queen's University (Kingston, Ont.))en
dc.date2008-09-24 09:49:35.462en
dc.date.accessioned2008-09-25T12:33:21Z
dc.date.available2008-09-25T12:33:21Z
dc.date.issued2008-09-25T12:33:21Z
dc.identifier.urihttp://hdl.handle.net/1974/1474
dc.descriptionThesis (Master, Mathematics & Statistics) -- Queen's University, 2008-09-24 09:49:35.462en
dc.description.abstractIn this thesis we describe how the balancing of the $\operatorname{Tor}$ functor can be used to compute the minimal free resolution of a graded module $M$ over the polynomial ring $B=\mathbb{K}[X_0,\dots,X_m]$ ($\mathbb{K}$ a field $X_i$'s indeterminates). Using a correspondence due to R. Stanley and M. Hochster, we explicitly show how this approach can be used in the case when $M=\mathbb{K}[S]$, the semigroup ring of a subsemigroup $S\subseteq \mathbb{N}^l$ (containing $0$) over $\mathbb{K}$ and when $M$ is a monomial ideal of $B$. We also study the class of affine semigroup rings for which $\mathbb{K}[S]\cong B/\mathfrak{p}$ is the homogeneous coordinate ring of a monomial curve in $\mathbb{P}^n_{\mathbb{K}}$. We use easily computable combinatorial and arithmetic properties of $S$ to define a notion which we call stabilization. We provide a direct proof showing how stabilization gives a bound on the $\mathbb{N}$-graded degree of minimal generators of $\mathfrak{p}$ and also show that it is related to the regularity of $\mathfrak{p}$. Moreover, we partition the above mentioned class into three cases and show that this partitioning is reflected in how the regularity is attained. An interesting consequence is that the regularity of $\mathfrak{p}$ can be effectively computed by elementary means.en
dc.format.extent737320 bytes
dc.format.mimetypeapplication/pdf
dc.languageenen
dc.language.isoenen
dc.relation.ispartofseriesCanadian thesesen
dc.rightsThis publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.en
dc.subjectCommutative Algebraen
dc.subjectCombinatoricsen
dc.titleBetti numbers and regularity of projective monomial curvesen
dc.typethesisen
dc.description.degreeMasteren
dc.contributor.supervisorRoberts, Leslie G.en
dc.contributor.departmentMathematics and Statisticsen


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