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Tangent cones of monomial curves /

by Sammartano, Alessio (AleSammy) [aut]; D'Anna, Marco [ths].
Material type: materialTypeLabelBookPublisher: Catania : Scuola Superiore di Catania, 2013Description: 57 p. : ill. ; 30 cm.Subject(s): ARMA | Algebra -- Rings | Curves, Algebraic | Computational algebra
Contents:
Introduction -- Preliminaries -- Cohen-Macaulayness and other properties -- Complete intersection property of the tangent cone -- Complete intersection numerical semigroups -- Conclusions -- Acknowledgements -- Appendix A : Implementation of algorithms in GAP -- Bibliography.
Dissertation note: Tesi di diploma di 2° livello per la Classe delle Scienze Sperimentali Diploma di 2° livello Scuola Superiore di Catania, Catania, Italy 2013 A.A. 2012/2013 Abstract: We investigate the main properties of the tangent cone $gr_m (R)$ of the local ring of a monomial curve $(R,m)$. After recalling the main results on the Cohen-Macaulayness, Gorensteinness and Buchsbaumness of $gr_m (R)$, we give four equivalent conditions for $gr_m (R)$ to be a complete intersection. In order to state our main theorem, we introduce two new classes of numerical semigroups. We study the relations among the various classes of complete intersection numerical semigroups present in literature. Finally, we implement our criteria in the computer algebra system GAP.
List(s) this item appears in: Tesi di Laurea, Diploma, Dottorato, Master
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Sala B : Armadio Tesi THS_2013 512.4 S189 (Browse shelf) 1 Available

Tesi di diploma di 2° livello per la Classe delle Scienze Sperimentali Diploma di 2° livello Scuola Superiore di Catania, Catania, Italy 2013 A.A. 2012/2013

Includes bibliographical references (p. 55-57).

Introduction -- Preliminaries -- Cohen-Macaulayness and other properties -- Complete intersection property of the tangent cone -- Complete intersection numerical semigroups -- Conclusions -- Acknowledgements -- Appendix A : Implementation of algorithms in GAP -- Bibliography.

Tesi discussa il 20/6/2013.

We investigate the main properties of the tangent cone $gr_m (R)$ of the local ring of a monomial curve $(R,m)$. After recalling the main results on the Cohen-Macaulayness, Gorensteinness and Buchsbaumness of $gr_m (R)$, we give four equivalent conditions for $gr_m (R)$ to be a complete intersection. In order to state our main theorem, we introduce two new classes of numerical semigroups. We study the relations among the various classes of complete intersection numerical semigroups present in literature. Finally, we implement our criteria in the computer algebra system GAP.

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