Homological and combinatorial properties of toric face rings

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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://repositorium.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

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