Quivers of sections on toric orbifolds

Details Quivers of sections on toric orbifolds Quivers of sections on toric orbifolds

2010-12-13

arxiv.org/abs/1012.2851v3

Journal of Algebra 349 (2012) 128-149

Mathematics

Algebraic Geometry

24 pages; minor change to the title; final version

Scientific paper

Starting from a collection of line bundles on a projective toric orbifold 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 a finite abelian subgroup G of SL(n,k) where n is less than or equal to 3.

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