On Partial Regularities and Monomial Preorders

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Title: On Partial Regularities and Monomial Preorders
Authors: Nguyen, Thi Van Anh
Thesis advisor: Prof. Dr. Tim Römer
Thesis referee: Prof. Dr. Ngo Viet Trung
Abstract: 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
Subject Keywords: 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
Issue Date: 28-Jun-2018
License name: Namensnennung-NichtKommerziell-KeineBearbeitung 3.0 Deutschland
License url: http://creativecommons.org/licenses/by-nc-nd/3.0/de/
Type of publication: Dissertation oder Habilitation [doctoralThesis]
Appears in Collections:FB06 - E-Dissertationen

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