Quivers of sections on toric orbifolds

作者：Abdelgadir Tarig M H^*

来源：Journal of Algebra, 2012, 349(1): 128-149.

DOI：10.1016/j.jalgebra.2011.08.033

• Projective stacks
• Toric stacks
• Quiver representations
• McKay correspondence

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 subset of SL(n, k) where n %26lt;= 3.

• 出版日期2012-1-1