Title:	On graded ideals over the exterior algebra with applications to hyperplane arrangements
Authors:	Thieu, Dinh Phong
Thesis advisor:	Prof. Dr. Tim Römer
Thesis referee:	Prof. Dr. Uwe Nagel
Abstract:	Graded ideals over the polynomial ring are studied deeply with a huge of methods and results. Over the exterior algebra, there are not much known about the structures of minimal graded resolutions, Gröbner fans of graded ideals or the Koszul property of algebras defined by graded ideals. We study componentwise linearity, linear resolutions of graded ideals as well as universally, initially and strongly Koszul properties of graded algebras defined by a graded ideals over the exterior algebra. After that, we apply our results to Orlik-Solomon ideals of hyperplane arrangements and show in which way the exterior algebra is useful in the study of related combinatorial objects.
URL:	https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2013092311626
Subject Keywords:	Exterior Algebra; Componentwise linear; Orlik-Solomon Algebra; Koszul algebras
Issue Date:	23-Sep-2013
Type of publication:	Dissertation oder Habilitation [doctoralThesis]
Appears in Collections:	FB06 - E-Dissertationen

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