Resumen de Spanning subspace configurations

Brendon Rhoades

• A spanning configuration in the complex vector space {{\mathbb {C}}}^k is a sequence (W_1, \dots , W_r) of linear subspaces of {{\mathbb {C}}}^k such that W_1 + \cdots + W_r = {{\mathbb {C}}}^k. We present the integral cohomology of the moduli space of spanning configurations in {{\mathbb {C}}}^k corresponding to a given sequence of subspace dimensions. This simultaneously generalizes the classical presentation of the cohomology of partial flag varieties and the more recent presentation of a variety of spanning line configurations defined by the author and Pawlowski. This latter variety of spanning line configurations plays the role of the flag variety for the Haglund–Remmel–Wilson Delta Conjecture of symmetric function theory.