Small rational model of subspace complement (Q2781392)

The cohomology of the complement of an arrangement of hyperplanes or subspaces of a complex vector space gives a useful handle on the combinatorics of the arrangement. In this paper, starting from a construction of \textit{C. De Concini} and \textit{C. Procesi} [Sel. Math., New Ser. 1, No. 3, 459-494 (1995; Zbl 0842.14038)] a relatively small differential graded algebra is obtained from the lattice of intersections of the subspaces in the arrangement together with their codimensions. The rational cohomology ring of the complement of the union of the subspaces in the arrangement is then obtained from the combinatorial information. In two special cases, that in which the lattice of intersections of the subspaces of the arrangement is geometric as well as that of the \(k\)-equal arrangements studied by \textit{A. Björner} and \textit{V. Welker} [Adv. Math. 110, No. 2, 277-313 (1995; Zbl 0845.57020], the computations are done more explicitly.