A congruence modulo four in real Schubert calculus
Abstract
We establish a congruence modulo four in the real Schubert calculus on the Grassmannian of mplanes in 2mspace. 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2012
 DOI:
 10.48550/arXiv.1211.7160
 arXiv:
 arXiv:1211.7160
 Bibcode:
 2012arXiv1211.7160H
 Keywords:

 Mathematics  Algebraic Geometry;
 14N15;
 14P99
 EPrint:
 24 pages