Mori dream spaces as fine moduli of quiver representations

QA Mathematics

Winn, Dorothy ; Craw, Alastair

University:University of Glasgow

Department:School of Mathematics and Statistics

关键词: Algebraic Geometry, Algebra, Geometry, Mori Dream Spaces, Noncommutative Algebra;   

Others  :  http://theses.gla.ac.uk/3367/1/2012winnphd.pdf

来源: University of Glasgow

【 摘 要 】

Mori Dream Spaces and their Cox rings have been the subject of a great deal of interest since theirintroduction by Hu–Keel over a decade ago. From the geometric side, these varieties enjoy theproperty 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 interestingproblem in itself. Examples include Q-factorial projective toric varieties, spherical varieties and logFano varieties of arbitrary dimension. In this thesis we use the representation theory of quivers tostudy multigraded linear series on Mori Dream Spaces. Our main results construct Mori DreamSpaces as fine moduli spaces of ϑ-stable representations of bound quivers for a special stabilitycondition ϑ, thereby extending results of Craw–Smith for projective toric varieties.