Chern Class Formulas for Quiver Varieties Anders Skovsted Buch and William Fulton

This is a closed subscheme ofX ; locally, where the bundles are trivial, this is defined by vanishing of the minors of size rij +1 in the product of matrices giving the map φj ◦ · · · ◦ φi+1 from Ei to Ej , for all i < j. Not all rank conditions give reasonable loci. Those that do—and the only ones we will consider—are characterized by the conditions rij ≤ ri,j−1 and rij ≤ ri+1,j for all i < j, and ri+1,j−1 − ri,j−1 − ri+1,j + rij ≥ 0 for all i < j − 1, (1.2)