osnaDocs: Affine Monoids, Hilbert Bases and Hilbert Functions

Affine Monoids, Hilbert Bases and Hilbert Functions

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https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2003071115

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DC Field	Value	Language
dc.contributor.advisor	Prof. Dr. Winfried Bruns
dc.creator	Koch, Robert
dc.date.accessioned	2010-01-30T14:50:30Z
dc.date.available	2010-01-30T14:50:30Z
dc.date.issued	2003-07-11T12:04:51Z
dc.date.submitted	2003-07-11T12:04:51Z
dc.identifier.uri	https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2003071115	-
dc.description.abstract	The aim of this thesis is to introduce the reader to the theory of affine monoids and, thereby, to present some results. We therefore start with some auxiliary sections, containing general introductions to convex geometry, affine monoids and their algebras, Hilbert functions and Hilbert series. One central part of the thesis then is the description of an algorithm for computing the integral closure of an affine monoid. The algorithm has been implemented, in the computer program `normaliz´; it outputs the Hilbert basis and the Hilbert function of the integral closure (if the monoid is positive). Possible applications include: finding the lattice points in a lattice polytope, computing the integral closure of a monomial ideal and solving Diophantine systems of linear inequalities. The other main part takes up the notion of multigraded Hilbert function: we investigate the effect of the growth of the Hilbert function along arithmetic progressions (within the grading set) on global growth. This study is motivated by the case of a finitely generated module over a homogeneous ring: there, the Hilbert function grows with a degree which is well determined by the degree of the Hilbert polynomial (and the Krull dimension).	eng
dc.language.iso	eng
dc.subject	affine monoid
dc.subject	integral closure
dc.subject	normalization
dc.subject	Hilbert basis
dc.subject	Hilbert function
dc.subject	affine monoid algebra
dc.subject	semigroup ring
dc.subject.ddc	510 - Mathematik	ger
dc.title	Affine Monoids, Hilbert Bases and Hilbert Functions	eng
dc.type	Dissertation oder Habilitation [doctoralThesis]	-
thesis.location	Osnabrück	-
thesis.institution	Universität	-
thesis.type	Dissertation [thesis.doctoral]	-
thesis.date	2003-05-26T12:00:00Z	-
elib.elibid	223	-
elib.marc.edt	fangmeier	-
elib.dct.accessRights	a	-
elib.dct.created	2003-06-06T11:47:27Z	-
elib.dct.modified	2003-07-11T12:04:51Z	-
dc.contributor.referee	Prof. Dr. Udo Vetter
dc.subject.msc	13B22	eng
dc.subject.msc	13D40	eng
dc.subject.msc	13P99	eng
dc.subject.msc	20M25	eng
dc.subject.msc	52B20	eng
dc.subject.dnb	27 - Mathematik	ger
vCard.ORG	FB6	ger
Appears in Collections:	FB06 - E-Dissertationen

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