2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68219We study the space ${\mathcal X}^{d}(G)$ of pictures of a graph $G$ in complex projective $d$-space. The main result is that the homology groups (with integer coefficients) of ${\mathcal X}^{d}(G)$ are completely determined by the Tutte polynomial of $G$. One application is a criterion in terms of the Tutte polynomial for independence in the {\it $d$-parallel matroids} studied in combinatorial rigidity theory. For certain special graphs called \defterm{orchards}, the picture space is smooth and has the structure of an iterated projective bundle. We give a Borel presentation of the cohomology ring of the picture space of an orchard, and use this presentation to develop an analogue of the classical Schubert calculus.LaTeX (uses xypic package), 22 pages. Final version, to appear in Advances in Mathematics. The title has been changed slightly, the exposition improved, the material in Section 6 clarified, and some open problems addedCombinatoricsAlgebraic GeometryAlgebraic Topology05C10 (Primary) 05B35, 14N20, 52C35 (Secondary)text