A Combinatorial Study on Quiver Varieties

Details A Combinatorial Study on Quiver Varieties A Combinatorial Study on Quiver Varieties

2005-10-21

arxiv.org/abs/math/0510455v2

Mathematics

Algebraic Geometry

26 pages, 2 figures, (v2) abstract and introduction changed, comments and references added, typos corrected

Scientific paper

This is an expository paper which has two parts. In the first part, we study quiver varieties of affine A-type from a combinatorial point of view. We present a combinatorial method for obtaining a closed formula for the generating function of Poincare polynomials of quiver varieties in rank 1 cases. Our main tools are cores and quotients of Young diagrams. In the second part, we give a brief survey of instanton counting in physics, where quiver varieties appear as moduli spaces of instantons. We discuss combinatorial aspects of its recent developments.

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