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Title: Mori dream spaces as fine moduli of quiver representations
Author: Winn, Dorothy
ISNI:       0000 0004 2715 1749
Awarding Body: University of Glasgow
Current Institution: University of Glasgow
Date of Award: 2012
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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.
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics