A congruence modulo four in real Schubert calculus

Nickolas Hein, Frank Sottile, Igor Zelenko

Published 2012-11-30, updated 2013-12-02Version 3

We establish a congruence modulo four in the real Schubert calculus on the Grassmannian of m-planes in 2m-space. This congruence holds for fibers of the Wronski map and a generalization to what we call symmetric Schubert problems. This strengthens the usual congruence modulo two for numbers of real solutions to geometric problems. It also gives examples of geometric problems given by fibers of a map whose topological degree is zero but where each fiber contains real points.