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