Intersection cohomology of type-A toric varieties

Type-A toric varieties may be obtained as GIT quotients with respect to a torus action with weights corresponding to roots of the group <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>S</mml:mi> <mml:mi>L</mml:mi> <mml:mo>(</mml:mo> <mml:mi>k</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> for some <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> . These varieties appear in various important applications, in particular, as normal cones to strata in moduli spaces of vector bundles. In this paper, we describe the intersection Betti numbers of these varieties, and those of some associated projective varieties. We present an elegant combinatorial model for these numbers, and, using the work of Hausel and Sturmfels, we show that the relevant intersection cohomology groups are endowed with a canonical product structure.