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Mori dream spaces as fine moduli of quiver representations

Winn, Dorothy (2012) Mori dream spaces as fine moduli of quiver representations. PhD thesis, University of Glasgow.

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Abstract

Mori Dream Spaces and their Cox rings have been the subject of a great deal of interest since their introduction by Hu–Keel over a decade ago. From the geometric side, these varieties enjoy the property that all operations of the Mori programme can be carried out by variation of GIT quotient, while from the algebraic side, obtaining an explicit presentation of the Cox ring is an interesting problem in itself. Examples include Q-factorial projective toric varieties, spherical varieties and log Fano varieties of arbitrary dimension. In this thesis we use the representation theory of quivers to study multigraded linear series on Mori Dream Spaces. Our main results construct Mori Dream Spaces as fine moduli spaces of ϑ-stable representations of bound quivers for a special stability condition ϑ, thereby extending results of Craw–Smith for projective toric varieties.

Item Type: Thesis (PhD)
Qualification Level: Doctoral
Keywords: Algebraic Geometry, Algebra, Geometry, Mori Dream Spaces, Noncommutative Algebra
Subjects: Q Science > QA Mathematics
Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Supervisor's Name: Craw, Dr. Alastair
Date of Award: 2012
Depositing User: Ms Dorothy Winn
Unique ID: glathesis:2012-3367
Copyright: Copyright of this thesis is held by the author.
Date Deposited: 07 May 2012
Last Modified: 10 Dec 2012 14:06
URI: http://theses.gla.ac.uk/id/eprint/3367

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