On Partial Regularities and Monomial Preorders

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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://repositorium.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
Enthalten in den Sammlungen:FB06 - E-Dissertationen

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