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Quivers of sections on toric Deligne-Mumford stacks

Abdelgadir, Tarig M.H. (2011) Quivers of sections on toric Deligne-Mumford stacks. PhD thesis, University of Glasgow.

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Abstract

Starting from a collection of line bundles on a projective toric DM stack X, we introduce a stacky analogue of the classical linear series. Our first main result extends work of King by building moduli stacks of refined representations of labelled quivers. We associate one such stack to any collection of line bundles on X to obtain our notion of a stacky linear series; as in the classical case, X maps to the ambient stack by evaluating sections of line bundles in the collection. As a further application, we describe a finite sequence of GIT wall crossings between [A^n/G] and G-Hilb(A^n) for G a subgroup of SL(n,\kk) for n less than or equal to 3.

Item Type: Thesis (PhD)
Qualification Level: Doctoral
Keywords: Toric stacks, quiver representations, McKay correspondence.
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: June 2011
Depositing User: Mr. Tarig Abdelgadir
Unique ID: glathesis:2011-06-2725
Copyright: Copyright of this thesis is held by the author.
Date Deposited: 04 Jul 2011
Last Modified: 10 Dec 2012 13:59
URI: http://theses.gla.ac.uk/id/eprint/2725

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