Homological and combinatorial properties of toric face rings
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https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2012082110274
https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2012082110274
Title: | Homological and combinatorial properties of toric face rings |
Other Titles: | Homologische und kombinatorische Eigenschaften torischer Seitenringe |
Authors: | Nguyen, Dang Hop |
Thesis advisor: | Prof. Dr. Tim Römer |
Thesis referee: | Prof. Dr. Aldo Conca |
Abstract: | Toric face rings are a generalization of Stanley-Reisner rings and affine monoid rings. New problems and results are obtained by a systematic study of toric face rings, shedding new lights to the understanding of Stanley-Reisner rings and affine monoid rings. We study algebra retracts of Stanley-Reisner rings, in particular, classify all the $\mathbb{Z}$-graded algebra retracts. We consider the Koszul property of toric face rings via Betti numbers and properties of the defining ideal. The last chapter is devoted to local cohomology of seminormal toric face rings and applications to singularities of toric face rings in positive characteristics. |
URL: | https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2012082110274 |
Subject Keywords: | Toric face rings; Stanley-Reisner rings; Koszul property; Algebra retracts; Seminormal rings; Local cohomology |
Issue Date: | 21-Aug-2012 |
Type of publication: | Dissertation oder Habilitation [doctoralThesis] |
Appears in Collections: | FB06 - E-Dissertationen |
Files in This Item:
File | Description | Size | Format | |
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thesis_nguyen.pdf | Präsentationsformat | 583,54 kB | Adobe PDF | thesis_nguyen.pdf View/Open |
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