The space of triangles, vanishing theorems, and combinatorics

We consider compactifications of (Pn)3 \ boolean OR Delta(ij), the space of triples of distinct points in projective space. One such space is a singul ar variety of configurations of points and lines; another is the smooth com pactification of Fulton and MacPherson; and a third is the triangle space o f Schubert and Semple. We compute the sections of line bundles on these spaces, and show that they are equal as GL(n) representations to the generalized Schur modules associ ated to "bad" generalized Young diagrams with three rows (Borel-Weil theore m). On the one hand, this yields Weyl-type character and dimension formulas for the Schur modules; on the other, a combinatorial picture of the space of sections. Cohomology vanishing theorems play a key role in our analysis, (C) 1999 Academic Press.