On Partial Regularities and Monomial Preorders

Bitte benutzen Sie diese Kennung, um auf die Ressource zu verweisen:
https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2018062823
Open Access logo originally created by the Public Library of Science (PLoS)
Titel: On Partial Regularities and Monomial Preorders
Autor(en): Nguyen, Thi Van Anh
Erstgutachter: Prof. Dr. Tim Römer
Zweitgutachter: Prof. Dr. Ngo Viet Trung
Zusammenfassung: My PhD-project has two main research directions. The first direction is on partial regularities which we define as refinements of the Castelnuovo-Mumford regularity. Main results are: relationship of partial regularities and related invariants, like the a-invariants or the Castelnuovo-Mumford regularity of the syzygy modules; algebraic properties of partial regularities via a filter-regular sequence or a short exact sequence; generalizing a well-known result for the Castelnuovo-Mumford regularity to the case of partial regularities of stable and squarefree stable monomial ideals; finally extending an upper bound proven by Caviglia-Sbarra to partial regularities. The second direction of my project is to develop a theory on monomial preorders. Many interesting statements from the classical theory of monomial orders generalize to monomial preorders. Main results are: a characterization of monomial preorders by real matrices, which extends a result of Robbiano on monomial orders; secondly, leading term ideals with respect to monomial preorders can be studied via flat deformations of the given ideal; finally, comparing invariants of the given ideal and the leading term ideal with respect to a monomial preorder.
URL: https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2018062823
Schlagworte: partial regularities, monomial preorders, Castelnuovo-Mumford regularity, filter-regular sequences, Local Duality Theorem, a-invariants, b-invariants, Betti-numbers, leading term ideals, flat deformations, weight orders
Erscheinungsdatum: 28-Jun-2018
Lizenzbezeichnung: Namensnennung-NichtKommerziell-KeineBearbeitung 3.0 Deutschland
URL der Lizenz: http://creativecommons.org/licenses/by-nc-nd/3.0/de/
Publikationstyp: Dissertation oder Habilitation [doctoralThesis]
Enthalten in den Sammlungen:FB06 - E-Dissertationen

Dateien zu dieser Ressource:
Datei Beschreibung GrößeFormat 
thesis_nguyen.pdfPräsentationsformat493,3 kBAdobe PDF
thesis_nguyen.pdf
Miniaturbild
Öffnen/Anzeigen


Diese Ressource wurde unter folgender Copyright-Bestimmung veröffentlicht: Lizenz von Creative Commons Creative Commons