2013/08/20 by Nickolas Hein, Christopher J. Hillar, Hein, Nickolas +3
Mathematics · #14N15 #14P99 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14N15 #msc:14P99
paper · pdf · doi:10.48550/arxiv.1308.4381
22 pages
arxiv created 2013/08/20 · arxiv updated 2013/08/21
We describe a large-scale computational experiment to study structure in the numbers of real solutions to osculating instances of Schubert problems. This investigation uncovered Schubert problems whose computed numbers of real solutions variously exhibit nontrivial upper bounds, lower bounds, gaps, and a congruence modulo four. We present a family of Schubert problems, one in each Grassmannian, and prove their osculating instances have the observed lower bounds and gaps.